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IN MEMORIAM 
FLORIAN CAJORl 




LOGARITHMIC, TRIGONOMETRIC, 



AND OTHER 



MATHEMATICAL TABLES. 



HENRY H. LUDLOW, 

First Lieutenant, Third Artillery:, U. S. Army, 
WITH THE CO-OPERATION OF 

EDGAR W. BASS, 

Professor of Mathematics in the U. S. Military Academy. 



NEW YORK: 

JOHN WILEY & SONS, 

53 East Tenth Street. 
1891. 



Copyright, i8go, 
HENRY H. LUDLOW. 



ROBERT DRU51M0ND, ^'^^^^ ^^'>^' 

Elect rotyper. Printer a, 

444 & 446 Pearl Street, 326 Pearl Street, 
New York. ^<''" ^''^^- 



PREFACE. 



In the accompanying tables, greater accuracy without in- 
creased space or labor is attained by using a mark [^-v] to repre- 
sent the addition of half a unit to any final figure over which it 
may be placed, each logarithmic and trigonometric value being 
thus tabulated to the nearest half-unit. 

Accuracy in tabulated values has been sought for by careful 
comparison with the tables of Schron, Bruhn, and Bremiker. 

Acknowledgment is due Lieutenant John A. Lundeen, 4th 
U. S. Artillery, for assistance in proof-reading. 

Henry H. Ludlow. 

New York City, April 15, 1890. 



CONTENTS. 



DESCRIPTION AND EXPLANATION OF TABLES 



PAGE 



Table I. — Logarithms of Numbers i 

Table II. — Important Constants and their Logarithms, . 7 

Tables III. and IV.— Logarithms of Trigonometric Func- 
tions, 8 

Table V.— Natural Sines, Cosines, Tangents and Cotan- 
gents, 19 

Table VI. — Squares, and Square Roots of Numbers, . 24 

Trigonometric Formulae 24 



TABLES I TO VI. 



EXPLANATION OF THE TABLES. 



TABLE I. 

LOGARITHMS OF NUMBERS. 

1. Contents and Arrangement. Table I. contains the man- 
tissas of the common logarithms of integers from i to 11009 
inclusive. 

The mantissas are given to 5 decimal places, except for 
integers from loooo to 11009, for v^hich they are given to 6 places. 

Since mantissas are, in general, incommensurable with unity, 
figures beyond the last place in the table are omitted. When 
the omitted part is 5 or more, and less than f , of the tabular unit 
(i.e. the unit of the last place of the table), the symbol --^, called 
half-mark, is placed over the last figure, indicating that \ the 
tabular unit should be added. When the omitted part is f or 
more of the tabular unit, the last figure has been increased by 
unity. 

Thus, 32 201 24 is tabulated 32 201 

18 041 26 " " 18 041 

40 908 74 " " 40 903 

51 321 76 '' " 51322 

The half-mark is used to reduce the error due to omitting 
part of the mantissa, without increasing the size of the table. 
It limits such errors to \ the tabular unit. 

On page i integers from i to 100 are arranged in order in 
columns. On the right of each number is its logarithm. 

On pages 2 to 21, inclusive, integers from 1000 to 11009 are 
given with the mantissas of their logarithms. 



2 EXPLANATION OF THE TARI.ES. 

All, except the last figure of each number, appear in the left- 
hand columns, arranged in order downv/ard; and the last figure 
of each is in the top and bottom horizontal lines, both of which 
begin with o and increase toward the right. 

In the column headed o the complete mantissas are given 
The last three figures are printed in full, but the first two are 
not when they are the same as the corresponding ones above. 
In the other columns the last three figures only of the mantissas 
are printed, the others being supplied from the column headed o 
on the same horizontal line or above it, except where an asterisk 
occurs, in which case the first two figures lie in the line next 
below. 

By this arrangement integers from loo to iioo form the left- 
hand columns of pages 2 to 21, and immediately to the right of 
each, in the column headed o, is the mantissa of its logarithm, 
since the mantissa is not affected by multiplying the number by 10. 

2. To find the Logarithm of any Positive Number. Conceive 
the decimal point in the number to be moved, if necessary, so as 
to give an integral part of 4 places. 

If the auxiliary number thus formed is entire, take the man- 
tissa directly from the table. 

If the auxiliary number has a fractional part, take the man- 
tissa of its integral part, and to it add the product of the differ- 
ence between it and the next greater mantissa in the table, by 
the fractional part. This method is based upon the assumption 
that the mantissa changes uniformly with the number, which is 
not strictly correct, and the result is only a near approximation. 
The difference between two consecutive mantissas in the table is 
called the tabular differe?tce, and is denoted by D. 

The characteristic of the common logarithm of any number 
greater than unity is positive and one less than the number of 
places of figures in the integral part of the number. 

The characteristic of the common logarithm of any positive 
number less than unity is negative and numerically one greater 
than the number of consecutive zeros that immediately fol- 
low the decimal point w^hen the number is in the form of a 



I.OGARIl'H.MS OF NUMnERS. 3 

decimal fraction. In this case the negative ci^n is placed over 
the characteristic to show that it alone is nerjative, the mantissa 
being always positive ; thus, 

log 0.012 = 2.07918 = — 2 -|- .07918, 

and is frequently written 8.0791S — 10. 

Examples. 

1. Find log 46.75. The auxiliary number is 4675. Opposite 
to 467, left-hand column, and from the column headed 5 take 
978, to which prefix 66 from the column headed o, giving log 
46.75 — 1.66978. 

2. Find log 0.04679. Opposite to 467, from column headed 
9, take 015 = 0155, to which prefix 67 from the o column and 
line next below, giving log 0.04679 = 2.670155 or 8.670155 — 10. 

3. Find log 4.6793. log 4.679 = 0.67015 

D X .3 = 9 X .3 = 2.7 = 2 



log 4.6793 = 0.67018 

4. Find log 73.8142. log 73.81 = 1.86811 

6 X -42 = 2.52 = 2 

log 73-8142 = 1.86814 

To facilitate the multiplication of D by a decimal fraction, 
proportional parts of D are given in the column headed P. P., on 
the right of each page, from which the product may be taken. 

Thus, to determine 6 X .42 we have, from P. P. under 6, 

P. P. .4 = 2.4 

P.P. .02 = .12 

P. P. .42 = 2.52 or 2 

5. log 903091 = 5-95573- 6. log 839.372 = 2.92395. 

7. log .0043483 = 3.63832. 8. log .000025939 = 5-4I395- 

9. log 1. 00016 = 0.000069. i°- log .11001 18 = 1. 04144, 
(Use table beyond loooo.) 



4 EXPLANATION OF THE TABLES. 

3. To find the Number corresponding to any Logarithm. If 
the given mantissa is found in the table, take the correspond- 
ing auxiliary number ; if not, take the auxiliary number corre- 
sponding to the tabular mantissa nearest to, and smaller than, the 
given. Subtract the tabular mantissa from the given, and divide 
the difference by the corresponding tabular difference. Annex 
the quotient to the auxiliary number already found, and place 
the decimal point as indicated by the characteristic. 

The tables of proportional parts facilitate the determination 
of the quotient to be annexed. 

Examples. 

1. log N = 2.86935 N = 740.3 

2. log N = 2.86937 

.86935 = the next less tabular mantissa, giving 7402. 
difference =2 D = 6 

In P. P. under 6 we find 1.8 gives 3 
Hence, .18 " 03 
Therefore, 1.98 gives 33 

The auxiliary number is 740233, and N = 740.233 

3. log N = 1. 99841, N = .99635 

4. log N = 3.7i936> N = .0052404 

5. log N = 2.007329, N = .0101702 

(Use table beyond 1000.) 

General Properties of Logarithms. 

4. 1°. The logarithm of any product is equal to the sum of the 
logarithms of its factors. 

2°. The logarithm of any quotient is equal to the logarithm of the 
dividend ?ninus that of the divisor. 

3°. The logarithm of any power of any number is equal to the 
logarithm of the number multiplied by the exponent of the poiver. 

4°. The logarithm of any root of any number is equal to the loga- 
rithm of the number divided by the index of the root. 



LOGARITHMS OF NUMBERS. 



Applications. 

5. When the mantissa of a subtrahend is greater than that of 
the minuend, unity is added to that of the minuend and sub- 
tracted from its characteristic. 

Thus, log^ = log .0103 — log 97 

log .0103 = 2.01283 
" 97. = 1.98677 

.0103 - .010^ 

log =4.02606 ^ = .OCOI061S 

97 97 ^ 

6. To multiply or divide a logarithm with a negative char- 
acteristic, multiply or divide its characteristic and mantissa 
separately ; and in case of division, add to the characteristic the 
smallest negative integer necessary to make it exactly divisible 
by the divisor, and add the corresponding positive integer to 
the mantissa. 

Thus, 



log lr~) = 5 (1-97393) = 5 + 4-86967 = 1.86967. 
log rj^ = Y (^-97393) = 7 (7 + 6.97393) = 1.99627. 



£xera'ses. 

With logarithms determine: 

- 22 X 8^ 

I. 4/f = 1. 12473- 2. —j=- = 12I 

r 121 

3. 0.456 X 0.03217 = 0.0146697. 

4. (0.0567)^ = .000010336. 

1^.0009374 „ 33 

5. ^ = 1.7988. 

■♦/.0026193 



1-33 
15. O.OI024''°7 = 0.05267. 

1-7 



6 EXPLANATION OF THE TABLES. 

6. — 0.0124^ = 0.00000002364- 12. — 592.1"' = ^ 0.1190. 

7. - o.42i"3= _ 13.4015. 13.12^-37 =361.13. 

8. 79965000-J = 0.0023206. 14. — 72*^ = Imaginary. 

9. 1.2l6-r = 0.97245. 

10. 0.2042s ^0.4519. 

11. 0.000204~s = 16.99. 16. 0.00231 3-5 = 19.078. 

7. The Arithmetical Complement of a logarithm is the remain- 
der after subtracting it from 10. 

Thus, a. c. log N = 10 — log N. 

Hence, — log N = a. c. log N — 10. 

Therefore, a?zv logarithm may be subtracted by addi7ig its arith- 
metical complement minus 10. 

Examples. 

( + log .41'^. = i.6i';qi; 

'• '0«-^^^^^= +.og3o.. =3.43.. 

[ + a. c. log .002854 - 10 = 2 .54454 

5.64150 

, { + log 276.3 = 2.44138 

, /276.3X4-i924\ J T 1 T \ 

2. logf-^-^^ — 1 =< + log 41924 = 0.62246 

^ "^ . (^ + a. c. log 99. — 10 = 8.00435 ~ 10 

= 1.06818 

8. Negative Numbers have no common logarithms, but indi- 
cated operations upon their numerical values may be performed 
by logarithms, and the sign of the result determined by combin- 
ing the signs of the numbers and those of operation. To follow 
the signs through the logarithmic work, the subscript n is gen- 
erally written with its logarithm when the sign of a factor is 
negative. 



I. 



MATHEMATICAL CONSTANTS. y 

Examples. 
With logarithms determine: 

(— 109) (3027) ( - 41-3 ) log 109. = 2.03742,. 

(57-23) (-47-1) (2.3415)* log 3027. =3.48101 

log 41-3 = i-6i595« 
a. c. log 57.23 = 8.24237 - ID 
a. c. log 47.1 = 8.32698;, — 10 
a. c. log 2.3415 = 9.63055 — 10 

3-33424« 
Ans. — 2158.9 

87 1^ _ 0.056 _. ^/\W 

^' - 2.7856 = ^"9486. 3. (Z^ = 0.18795. 

(-1146)5(0.0051)' ^^ 



TABLE II. 

MATHEMATICAL CONSTANTS. 

Part I. gives the logarithmic constants M, — and ^ to 10 

places, with logarithms to 8 places. The auxiliary tables on the 
left enable us to find the Napierian logarithm of a number 
from its common logarithm without laborious multiplication. 
Thus § I, given log 321 = 2.50656, we have 

2. 4.60 517 oig 

•5 1-15 129 254 

.006 .01 381 551 

.0005 .00 115 129 

.00000 . .00 001 151 

.-. log^ 321 = 4.77 144 105 

In such computation it is usually sufficiently accurate to 
keep one place of figures more than is required in the result. 



8 EXPLANATION OF THE TABLES. 

The auxiliary table on the right is for the reverse of this pro- 
cess. 

Part II. gives circular and spherical constants to 8 places, 
with logarithms to 8 places. 

Part III. gives angular constants to 8 places, with their loga- 
rithms to 8 places. They are principally useful in changing the 
angular unit. 

TABLES III AND IV. 

LOGARITHMS OF SINES, COSINES, TANGENTS AND COTANGENTS. 

(The explanation of Table III follows that of Table IV.) 

10. Table IV contains the common logarithms of the sine, 
cosine, tangent and cotangent of all angles at intervals of i' from 
o° to 90°. 

Except the tangents from 45° to go'', and the cotangents from 
0° to 45°, each function is less than unity, and its common loga- 
rithm is negative. To avoid minus signs in the table, 10 is arbi- 
trarily added to each negative characteristic. 

The table is arranged with reference to the angles. Those 
from 0° to 45° are placed, in order, downward in the left-hand 
column of each page, with degrees at the top of the page ; those 
from 45° to 90°, in order, upward in the right-hand column, 
with degrees at the bottom of the page, each angle between 45° 
and 90° on the same line with its complementary angle. The 
values of the logarithmic functions, each on the same line with 
its angle, are arranged in columns with names at the top for 
angles between 0° and 45°, and at the bottom for angles between 
45 and 90 . 

Each column headed D gives the tabular difference — i e. dif- 
ference between consecutive tabulated values — for the column 
on its left. 

Let a be the angular interval, then na and (// + \) a are con- 
secutive angles of the table. By (6), Trigonometry, we have 

tan 7ia = , and tan (n -\- 1) a = 



cot na^ cot {11 -\- i) a'' 



LOGARITHiMS OF SINES, COSINES, TANGENTS AND COTANGENTS. 9 

tan {n -{- i) a _ cot fine ^ 
' ' tan na ~ cot (« + i) a' 

or, applying logarithms to both members, 

log tan (n -{- i) a — log tan na = log cot na — log cot {n -\- i) a. 

That is, t/ie logarithmic tangent and logarithmic cotangent have a cum- 
mon tabular difference. The column of their common differences 
is usually arranged between the columns of these logarithms. 

11. To find the Logarithmic Sine, Cosine, Tangent or Cotangent 
of any Angle 0. 

If is in the table, take the number on the same line with 
it, and from the proper column. Thus, 

log sin 19° 55' = 9-53231 — 10. log cos 19° 55' = 9-97321 — 10; 

log tan 19° 54' = 9.55870 — 10, log cot 19° 54' = 0.44129; 

log sin 66^ 19' = 9.96179 — 10, log cos 66° 19' = 9.60388 — 10; 

log tan 66"" 19' = 0.35791, log cot 66° 19' ^ 9.64209 — 10. 

If lies between two consecutive tabular angles, take the 
function for the lesser angle, and correct it by the approximate 
principle, that small changes of the angle are proportional to 
the corresponding changes of their logarithmic functions. Aux- 
iliary tables of proportional parts facilitate the solution of this 
proportion. Thus, to find log sin 73° 12' 53", and log cos 49° 
IZ 32 : 

log sin 73° 12' 9.98105 — 10, log cos 49° 33' 9.81210 — 10 

Diff. 4 P^P. 50" + Z-l Diff. 15 P.P. 30" - 7.5 

P.P. i" + .2 P.P. 2" -0.5 

log sin 73° 12' 53" 9.98109 — 10, log cos 49° T,i' 32" 9.81202 — 10 

The algebraic sign of the correction is determined by ob- 
serving whether or not the required function increases as the 
angle increases. The corrections are carried out one place of 
decimals farther than the numbers in the table, and the value 
of the total correction then taken to the nearest unit in the last 
place of the table. 



EXPLANATION OF THE TABLES. 



Examples. 

log sin 73° 29' i4"=:9.98i7i-io, log tan 37° 28'3i" = 9.88459-io; 
log cos 9°58'33" = 9-99338-io, log 00165° 21' 45" = 9.66i46- 10; 
logcot87°57'59" = 8.55o34-io, logtan65° 2i'45" = o.33854. 

If is not in the first quadrant, the function should be 
reduced to the first quadrant. The logarithm of its numerical 
value may then be taken from the table. Thus, 

sin 210" 17' = — sin 30° 17'. 

Hence, numerically, log sin 210° 17' = log sin 30° 17'; 

or, log sin 210° 17' = 9.70267 — 10. 

Similarly, log tan 115° 33' = log cot 25° i^'; 

or, log tan 115° n' = 0.32053. 

Similarly, log sin 115° n' = 9.95530 - 10. 

When it is necessary to consider the sign of a negative func- 
tion the subscript 71 is used. Thus, 

log sin 210° 17' = 9.70267^ — 10. 
log sin 115° i2>' = 9-9553° - lo- 
log tan 115° 33' = 0.32053,,. 

Examples. 



I. 


log sin 235° 19' 


n" 


= 


i.9i5o7„. 


2. 


log cos 329° 26' 


41" 


= 


1-93507. 


3- 


log tan 136° 14' 


22 


= 


1.98120,2. 


4- 


log cot 317° 2,Z' 


3j 


= 


o.o3885„. 


5- 


log sin — 37° 43' 05" 


= 


i.78659«. 


6. 


log cos — 430° 


22' 


=r 


1.52634. 


7- 


log cot — 




= 


0.23856. 


8. 


log cot I 




= 


1.80759. 


9- 


\7t 

log COS — ^:^— 

4 




= 


i.84948«. 


10. 


log tan — 8;r 




= 


— CO . 



LOGARITHMS OF SECANTS, COSECANTS, VERSINES AND COVERSINES. II 

12. To find the Logarithmic Secant, Cosecant, Versine and Cover- 
sine of any Angle 0. 

These are not given in the table, but from § 51, Trigonom- 
etry, we have 

sec = — — , cosec 



cos sin 0' 

vers 0=1— cos 0, covers = i — sin 0. 

Hence, 

log sec = — log cos 0, log cosec = — log sin 0, 
log vers = log (i — cos 0), log covers = log (i — sin 0). 
Thus, 

log sec 66° 19' = 10 — 9.60388 = 0.39612. 
log cosec 66° 19' = 10 — 9.96179 = 0.03821. 
log vers 66° 19' = log (r — 0.40168) = log 0.59832 
= 1-77693 = 9-77693 - 10. 
log covers 66° 19' = log (i — 0.91578) = log (0.08422) 
■ = 2.92541 = 8.92541 — 10. 

" Examples. 

1. log sec 12° 25' = 0.01028. 

2. log cosec 12° 25' = 0.66752. 

3. log vers ef 35' = 1-74437- 

4. log covers (iT,° 35' = i. 01878. 

5. log sec 235° 19' 30" = o.24494«. 

6. log cosec — 430° 22' = o.o26oi«. 

7. log vers (if- 7r) = 1.95630- 

8. log covers — 1.72 = 2.04571. 

9. log sec ^^— =0.15051. 

4 

, 2;r — 7 
10. log cosec = o.74893„. 



12 EXPLANATION OF THE TABLES. 

11. log sec 1.57079632 = — 00 . 

12. log covers (— 645") =2.53237. 

13. log covers 44° 22' = 1.47826. 

14. log vers 130'^ = 0.2 1558. 

15. log vers 27° 22' = 1.04887. 

16. log vers 15° = 2.53237. 

17. log covers 7° 31' 55" = 1.93898. 

Log vers and log covers may also be determined from (43), 
Trigonometry. 

vers (p = 2 sin'' J0, covers 0=2 sin^ i(9°° ~ ^)- 

Hence, 

log vers = log 2 -|- 2 log sin 40. 
log covers = log 2 -[- 2 log sin 4(90° — 0). 

13. To find from its Logarithmic Sine, Cosine, Tangent or Cotan- 
gent. — If the given value is not found in the proper column, take 
from the table the angle corresponding to the lesser of the two 
consecutive values between which it lies. Subtract this lesser 
value from the given value, and find the angular correction 
corresponding to this difference. The angular correction is' 
found by the same principle, and by a process the reverse of that 
used in finding the correction of a function for an intermediate 
angle. Thus, 

To find when log cos = 9.92657 — 10 
log cos 32° 24' =■ 9.92651 — 10 

-45" 

6 D 8 



32" 23' 15" 
If cos is positive, we have 

= 32° 23' 15", and = 360°- (32° 23' 15"). 

If cos is negative, we have 

= iSo°- (32^ 23' 15"), and = 180° + 32° 23' 15''). 



LOGARITHMS OF SIXES, COSINES, TANGENTS AND COTANGENTS. 13 

Examples. 
Find all positive values of <p <36o° : 

1. When log sin = 9.76541 — 10. 

Ans. 35° 38' 15" and 144° 21' 45". 

2. When log cos = 9.51 05 9„ — 10. 

Ans. 108" 54' 25" and 251° 5' 35". 

3. When log tan = 0.56644. 

Ans. 74° 49' 2" and 254° 49' 2". 

4. When log cot = 9.43263,, — 10. 

Ans. 105° 9' 6" and 285° 9' 6". 

14. To find from its Logarithmic Secant, Cosecant, Versine or 
Coversine. — By means of formulas §51, Trigonometry, logarithmic 
secants, cosecants, versines and coversines may be expressed in 
terms of logarithmic cosines or sines, from which may be 
found as above. Thus, 

Given log sec = 0.04891, 

we have 



cos 





I 


55" 
5" 


log cos 
- 0.04S9I 


0: 


9-95 


log se 
109 — 




sec 0' 
log cos 
26° 42' 

26° 41' 


10 






6 D 


6 



.-. 0=26° 41' 5" and zzz"" 18' 55". 

Similarly, may be determined from any of its trigonometric 
functions. Thus: 

Having vers = 1.2346, 



14 EXPLANATION OF THE TABLES. 

then, cos = i — vers = — 0.2346 

. •. log cos = log (o.2346)„ = 1.37033™ 



76° 26' 4 D 52 

_^' 

76" 25' 55" 

.-. 0=103° 34' 5" and 256° 25' 55". 

The required angle will be < 90°, or iSo°— 0, or iSo°-|- 0, 
or 360°— 0, according to the quadrant in which the trigonometric 
function lies. There will always be two positive angles less thaa 
360°. 

Exa}nples. 

Find all positive values of less than 360° : 

1. When log sec = .05846. 

Ans. 29° 4' o" and 330° 56' o". 

2. When log cosec = .02616. 

Ans. 70° 20' and 109° 40' 

3. When log vers = 9.04891 — 10. 

Ans. 27° 22' 5" and 332° 37' 55". 

4. When log covers = 9.93898 — 10. 

Ans. 7° 31' 55" and 172° 28' 5". 

Find in degree-measure from the table of logarithmic sines, 
etc., all positive values, less than 360°, for each of the following 
angles : 

5. sin - '[-.23]. Ans. 193° 17' 50", 346° 42' 10" 

6. cos-'f. Ans. 51° 19' 4", 308° 40' 56" 

7. tan-'[-f]. A71S. 141" 20' 25", 321° 20' 25" 

8. cot - '.72. Ans. 54° 14' 46", 234° 14' 46" 

9. sec - '[- 1.4]. Ans. 135° 35' 5", 224° 24' 55'' 
10. cosec ~ '3.5. Ans. i6° 36' 5", 163° 23' 55 



LOGARIIHMS OF SIXES, COSINES, TANGENTS AND COTANGENTS. 15 

11. vers - 'f A/is. 31° o' 12", 328° 59' 48". 

12. covers -'1.3. A;is. 342° 32' ss", ^97° 27' 27". 

13. cosec - '[± 5.758S]. A/is. 10°, 170'', 190°, 350", 

14. cosec - ' — 2. Affs. 210°, 330°. 

15. In seeking angles from the tables, extreme values of 
logarithmic functions may arise. 

If log sin = 0— 10= — 10, 

we have 

sin 0=10- '°, and = 10 - ^°. 

In which case is practically, though not absolutely, zero. 
With a radius of 100 miles it intercepts an arc of 

10 - s mi. = .00062 in. 

If log cos = — 10, 

is the complement of the value just considered, and is practi- 
cally 90°. 

If log tan = — 10, 

<p is practically zero. 

If log cot = — 10, 

0> is practically 90°. 

If log sin = 10 — 10 := o, sin = i and = 90°. 

If log cos (p = o, cos (p = I and = 0°. 

If log tan (p = o, tan = i and = 45°. 

If log cot (p — o, cot (p =z \ and = 45°. 

If log tan = 10, tan = io'°; .". cot = 10 -'°, 
and is practically 90°. 

If log cot = 10, cot = io'°; .-. tan = 10-"°, 
and is practically zero. 



l6 EXPLANATION OF THE TABLES. 

TABLE III. 

LOGARITHMIC SINES AND TANGENTS OF ANGLES 
LESS THAN 3°. 

16. It has been assumed that small changes in the angle are 
proportional to the corresponding changes of any one of its 
functions. If this approximate principle were exact, the tabular 
difference for each function would be constant, since it corre- 
sponds to a constant small change of angle. Hence the accuracy 
of this principle is the greater, the more slowly the tabular dif- 
ference changes. 

To insure sufficient accuracy of interpolation in finding loga- 
rithmic sines and tangents of small angles, and the reverse, 
the values of 

''tan 0\ 



r=ioc 



0' 



computed at intervals of i' from 0° to 3° (those of S and T being 
increased by 10), and are given in Table III. The first four 
figures of 7" and T' are the same as those of ^and S' respectively. 
These quantities change so slowly and regularly that the ordi- 
nary method of interpolation gives very accurate results. 

Given 0, to find log sin and log tan accurately, when 

0<3°. 

sin = 0" — 77^, and tan = —^\ 

.-. log sin = log 0" -f log (^^) = log 0" + S, 

log tan = log 0" + log (^-^) = log 0" + T. 

Hence, to find the logarithmic sine or tangent, add to the 
common logarithm of the number of seconds in 0, the correspond- 
ing value of S or T. 



LOGARITHMIC PINES AND TANGENTS OF ANGLES LESS THAN t' 



17 



The angles are expressed in degrees and minutes, also in 
seconds. 

Examples. 

I. Find accurately log sin 1° 7' 47". 3. Look in the table for 
1° 7' =4020". 

<p" = 4020" + 47".3 = 4o67".3, log 0" = 3.60930 

'S' 4-68554 — 10 



log sin 1° 7' 47".3 = 2.29485 
The ordinary method gives 2.29483 

2. Find accurately log sin 0° 42' 24". 7. Ans. 2.09120 

3. Find accurately log tan 1° 51' 21". 4. Ans. 2.51059 
To find log cot accurately, when is less than 3". 



Since 



cot = 



tan 



, we have 



log cot <p = — log tan 0, 

which may be found as above indicated. Thus, 

log cot 1° 51' 21". 4 =: 10 — 8.51059 = 1. 48941. 

When 87° < < 90°, find log cos and log cot by 
determining their equals, respectively, log sin (90° — 0) and 
log tan (90° — 0). 

17. Given log sin or log tan 0, to find accurately, when 

0<3°. 

The above method might be reversed, but the following is 
more convenient : 



0" = sin 



— and 0" = tan 



0' 



sin tan 0' 

.-. log 0" = log sin + log (gj— ^j = log sin + S', 

log 0" = log tan + log [~-^) = log tan 0+ r. 



l8 EXPLANATION OF THE TABLES. 

Hence, to find log cp" add S' to log sin 0, or T' to log tan 0; 
0" may then be found from Table I,* 

Examples. 
I. Given log tan = 7.55641 — 10, find accurately. 
lies between 720" = 12' and 780" = 13', both of which 
have the same value of T'. 

log tan 7-55641 — 10 
^' 5-31445 



log 0" = 2.87083 



2 Z? 5 

.-. 0" = 742".74 = o° 12' 22-75 

2. Given log sin = 6.83214 — 10, find accurately. 

Alls. 0° 2' 20". 14. 

3. Given log sin = 8.65815 — 10, find accurately, 

Ans. 2°36'3i''.3. 

4. Given long tan = 8.42973 — 10, find accurately. 

^/w. 1° 32' 26", 9. 

From log cot we have — log tan 0, from which may be 
determined. 

When 87° < < 90°, log cos and log cot equal, respec- 
tively, log sin (90° — 0) and log tan (90° — 0) from which 90° — 
may be found as above. 

* c- ^" ^So X 60 X 60 ^ 

* since (p = m, we have 

jr 

sin sin (b it . tan (b tan tt 

— and — 



0" 180X60X60 (p" (p 180X60X60 

tan 



TT limit sin (p 
Hence, ^., „ 21 

° [_ (p" 



~ lim 



_ 0' J 64800 



log ( 1 = 5.68557, the common initial value of 5 and T. 

\.648oo/ 

log I— ] = 4.31442, the common initial value of S' and 7". 



VALUES OF SINES, COSINES, ETC., OF ANGLES FROM O TO 90 . I9 

TABLE V. 

18. Contains the values of the si/it's, cosi/ics, tangents and cotan- 
gents of all angles at intervals of lo', from o° to 90°, computed to 
four decimal places. 

In the construction of this table, denote by x the angular 

sin .v 
interval in radians. Since .v is small, is near its limiting 

value, unity, and we have, approximately, 

sin .V = A- (t?)* 

Since the interval is 10', we have, approximately, 

.V = r-meas 10' = 0.00290S882 ^sin 10'. 
Hence, 

cos 10' = |/x — sin" 10' = 4^(1 ■\- sin 10') (i — sin 10'); 
or, cos 10' = 0,999995769. 

From (56) and (58), Trigonometry, by transposition, we have 
sin (of -j- /?) = 2 sin a cos ft — sin (o' — /5), 
cos (« + /5) = 2 cos a cos fi — cos {a — /?). 

* Since 7t = 3.14159265359, we have, by computing sin i", sin 10' and 
sin l' from (73), 

r-meas 1° = 0.0174533, sin 1° = 0.0174524; 

r-meas 10' = 0.002908S821, sin 10' = 0.0029088817; 

r-meas I ' =0.0002908882087, sin i' =0.0002908882082; 

hence, we see that sin x = at is accurate to the 5th place if x does not exceed l°, 
to the Sth place if x does not exceed 10', and to the nth place if x does not ex- 
ceed i'. 

Hence, we may write with practical accuracy, 

sin i' = r-meas i', and sin i" = r-meas i". 
If be any angle given in radians, and required in minutes or seconds, 

0' = -, and 0" = 



r-meas i' r-meas i 

or, reducing by the above approximate relations, 

0' = — ^,, and ' = —^,7. 
sin 1 sin I 



20 EXPLANATION OF THE TABLES. 

Put fS = lo', and then put a = lo', a = 20', a = 30', etc., in 
succession, giving 

sin 20' = 2 sin 10' cos 10' — sin o = 0.005S17739, 
sin 30' = 2 sin 20' cos 10' — sin 10' = 0.008726547, 
sin 40' = 2 sin 30' cos 10' — sin 20' = o. 01 1635256, 
etc. = etc = etc. 

cos 20' = 2 cos' 10' — cos O =: O.999983076, 

cos 30' =: 2 COS 20' cos lo' — COS lo' = O.99996192I, 

cos 40' = 2 COS 30' COS 10' — COS 20' — 0.999932306. 
etc. = etc. = etc. 

This process may be continued to 45°. As each computation 
depends on those preceding it, the work should be checked at 
intervals by separate computations. For this purpose (72), Trigo- 
nometry, may be written 

. sin ff — sin /i ^ 

sm (« + ^) = ___^__^- (sm a + sm /?) ; 

in which put 90° + a for a, giving, after reduction, 

cos «' — sin /? , • /p\ 

cos (a 4- p) = -. -r- (cos a 4- sm a). 

^ ' cos \a — P) ^ ' ' 

From these formulas we may recompute the sine and cosine 
of 2°, 3°, etc., by making /? = 1°, and in succession a- = 1°, or = 2°, 
etc. 

The tangejits and cotangents of angles from 0° to 45° may now 
be computed from their sines and cosines by (4) and (5), Trigo- 
nometry. 

The sines, cosines, tangents and cotangents of angles from 
45° to 90° are, respectively, the cosines, sines, cotangents and 
tangents of their complements, which are between 0° and 45°. 

The table is arranged with reference to the angles. Those 
from 0° to 45*^ are placed, in order, downward in the left-hand 
column of each page; those from 45" to 90°, in order, upward in 
the right-hand column, each angle between 45° and 90° on the 
same line with its complementary angle between 0° and 45°. 



VALUES OF SINES, COSINES, ETC., OF ANGLES, FROM O TO 90 . 21 

The values of the functions, each on the same line with its 
angle, are arranged in columns, with names at the top for angles 
between o° and 45°, and their complementary names at the 
bottom for the complementary angles between 45° and 90 '. 

Required functions or angles may be taken directly from the 
table if the given angles or functions correspond exactly with 
those in the table. 

If a given angle lies between two consecutive angles in ihe 
table, the required function may be interpolated by the method 
used in the table of common logarithms of numbers, assuming 
that small differences of the function are proportional to the 
corresponding differences of the angle. The solution of the 
proportion is facilitated by auxiliary tables of proportional parts y 
each headed with its tabular difference. 

Thus, to find sin 31° 27' and cot 47° 44', we have 

sin 31° 20' 0.5200 cot 47° 40' 0.91 10 

D. 25 P.P. 7' 17- D.* 53 P.P. 4' - 21.2 



sin 31° 27' 0.5217 cot 47° 44' 0.9089 

The reverse process is entirely analogous. Thus, to find 
cos -'0.3162, and tan -' i. 2014, seek in the table the nearest 
functions less than those given. 

cos-' 0.3162 tan-' 1. 2014 

cos 71° 40' 3145 tan 50° 10' 1.198S 



D. 27 ig D. 71 26 

-6' 16.S 3'.6 26 

^ ioX-^ = 3-6 



71^^ 34' 50° i3'.6 7? 

If the question relates to secant, cosecant, versed-sine or co- 
versed-sine, it may be reduced to a question of sine or cosine 
by (7). (8), (2) or (3), § 51, Trigonometry. 

If the given angle is not in the first quadrant its required 
function should be reduced to the first quadrant [§ 56, Trig.]. 
A required angle, if not restricted to the first quadrant, may be 

* The correction is negative, since the cotangent decreases as the angle 
increases. 



EXPLANATION OF THE TABLES. 



the angle, denoted by 0, taken from the table, or i8o° — 0, or 
i8o° + 0, or 360" — 0, depending upon the sign of the function. 
Two values of 0, both positive and less than 360°, may always 
be found. [Trigonometry.] 

Examples. 

I. Find the following functions : 
sin 53° 25'.8 =0.8031. cos35i°38'.4 = 0.9894 

cos 61° 53'. 2 = 0.4712 



sec 63° 22'. 2 = 2.2309 
cosec 37° 49'.7 = 1.6305 
vers 31° 10'. 3 = 0.1444 



covers 72° 12'. 5 = 0.047* 



tan 308° 21'. 6 = — 1.2635 
cot 188° 26'.i = — 6.7441 



sec 292° 35'. 5 = 2.6031. 

cosec 149° 39'. I = 1.9792. 

vers 152° 43'.3 = 1.8888. 

sin 244° 57'. I = — 0.9059. covers 263° 17.2 = 1.9931. 

2. Find the following inverse functions less than 90° : 
sin - ' 0.9842. Afis. 79° 48'. 
cot -I 0.4321. Ans. 66° 37'.8. 
sec -'3.7255. Ans. 74° 25'.9. 
cosec-' 1-5398. Ans. 40° 30'. 
vers -' 0.0125. Ans. 9° 4'. 5. 
covers - ' o 3964. Afis. 37° 7'. 7. 
vers - ' 0.8407. Ans. 80° 50'. 

3. Find for the following inverse functions all positive values 
less than 360° : 



cos - ' .6557 



49° I' 36' 
310 58 24 



r T ( 207° 12' 25 

Sin - ' I — 0.4572] = \ 

"- -* (332 47 35 

tan - ' [- 3] 



cot - ' 1.25 



108° 26' 6" 
288 26 6 

38° 39' 34'^ 
218 39 34 



f or 

^ 129 14 

vers - ' 1.6325 = J Z 

I 230 46 



covers - ' 0.23 11 



( 50° 15' 24 
( 129 44 



36 



VALUES OF SINES, COSINES, ETC., OF ANGLES FROM O TO 90°. 23 



70 S ^9 

sec- ' 2.9371 = -^ :i oj 

{ 289 54 21 

,r 1 ( 225° o' 45" 

cosec - ' L — 1.4139J = ^ 

( 3'4 59 15 
19. At the end of Table IV is a table for passing from sexa- 
gesimal to r-measure of any angle. Thus to find the r-measure 
of 264° 13' 58", we have 



200° 




3-490658 


60° 




1. 046197 


4° 




.069813 


10' 




.002909 


3' 




.000872 




50" 


.000342 




8" 


.000039 



264° 13' 58" = 4.610732 radians. 

The table may be easily reversed to obtain sexagesimal from 
r-measure. Thus to find the angle i : 

1. 000000 
50° 0.872664 



D. 


•127335 


r 


.122173 




.005162 


10" 


.002909 




.002253 


7' 


.002036 




.000217 


40" 


.000194 




.000023 


4" 


.000019 




4 


o".9 


4 



givmg57 17' 44". 9. 



24 EXPLANATION OF THE TABLES. 

20. Tabular Errors. — Considering the half-mark, the error of 
auv tiibulatcd value cannot exceed \ the tabular unit, but may be 
positive or negative. The correction for interpolating a value is 
subject to alike error. "Y\\^ error of any interpolated value, n^^- 
lecting that due to the method of interpolation, is the algebraic 
sum of these two errors and cannot exceed \ the tabular unit. 

The error of the sum of n interpolated numbers is the 
algebraic sum of their several errors, and cannot exceed 

n 

— tabular units. 

2 

A computed angle is liable to error due to error in the value 
of the logarithmic [or natural] function by which the angle is 
found from the table. An error of / tabular units gives an 

angular error of -^ times the angular interval of the table. This 

angular error is the less, the greater the value of D, or the more 
rapidly the function changes with respect to the angle. Hence, 
a rapidly changing function is preferable for the computation of 
angles. 

The tangent and cotangent of any angle change more rapidly 
than its sine and cosine. The sine changes more rapidly than 
the cosine for angles between o° and 45°; the cosine more rapidly 
than the sine for angles between 45° and 90". 

TABLE VI. 

21. Table VI contains the squares and square roots of integers 
from I to 1000 inclusive. 

Trigonometric Formul.<e 

are arranged for reference as follow: 

Chord of arc (pR = 2R sin |0. 

Height of arc (pR from its chord = R vers \(p. 

vers 0=1— cos <p. covers = i — sin 0. 



TRIGONOMETRIC FORMUL^t;. 



25 



sin 



cosec 



cos 
cot 0' 

COS tan 0. 

tan 



sec 


0' 






Vi 




cos^ 


0. 


i/l' 


+ cot* 
tan 


"0* 


v^ 


+ 


tan' 


<P 


Vsec' 


0- 


I 




sec 







V'^ 


[ — 


cos 


20 



COS 



sin 



tan 0" 

sin cot 0. 
cot 



2 sin 10 cos ^0. 

1 — 2 sin= (45° — ^0). 

2 sin' (45° + 10) -I 



2 tan 10 




sec 



cosec 0' 



V^i — sin" 0. 
I 



i/i + tan' 0' 
cot 



|/i -H cot' 0' 
-/cosec' 0—1 



cosec 

. /l + cos 20 



COS" i0 — sin 



■^ 1 , 



-n' |( 



1 — 2 sin" 

2 cos' 0-|- — I. 
cot 1^0 — tan |^( 



cot 10 + tan -|0* 



I - tan' (45° - i0) 
i + tan'(45°-i0) 



cot 10 + tan ^0 



I + tan tan ^0 

I — tan' ^0 
I -f- tan' 10 ' 



tan 



sin 



cot 



cos 

sin sec 0. 
sec 



cosec 0' 


Vsec" 0—1. 


I 


l^cosec' — 1 


sin 


1^1 — sin' 0' 


Vi — cos' 


cos 


^/l — cos 20 


I -f cos 2 


sin 20 


I + COS 20' 


I — COS 20 



sin 20 

cot 0—2 cot 20. 

2 tan 10 



I — tan' ^0 
2 



cot i0 — tan ^0' 

2 cot ^0 
cot' 10 — i' 



?6 TRIGONOMETRIC FORMULA. 

Functions of 2a, 3n and ^a. 

sin 20' = 2 sin a cos a. 

cos 2a = cos^ a — sin" o" = i — 2 sin^ a = 2 cos" a — I 
= 2 sin (45° — a) cos (45° — a). 
2 tan a sin « cos a 



tan 20" = 



I — tan' a sin (45" — a) cos (45° — a)' 



cot «- — I , ^ , ^ 

cot 20; — = i cot « — i tan a. 

2 cot « " 

versin 2a =2 i — cos 20' = 2 sin^ cr. 

coversin 20' = i — 2 sin a cos a = 2 sin*(45° — a). 

sec 2a = — 5 -r-i — — 4^ sec (45° — a) cosec (45° — a). 

cos « — sin a " ^ ^ ' 

cosec 20; = — r- = i sec a; cosec a. 

2 sin or cos a 

sin 30; = 3 sin a — 4 sin^ cr. cos 30? = 4 cos' «r — 3 cos a. 

•^ tan rt" — tan' a cot' or — ^ cot a 

tan 3^ = i^ -„ . cot ^a = -— •. 

1 — 3 tan a 3 cot a — i 

sin 40' = 4 sin a cos a — S sin^ a cos a. 

cos 40- = 8 cos^ a — S cos^ tf + i- 

4 tan a — 4 tan' a cot* or — 6 cot a -\- i 

tan 4a = 5 r~L — i — • cot 4a = 5 — -. 

1—6 tan a -\- tan a 4 cot a — 4 cot a 

Functions of ^. 



. a . i/i — cos a 

sin - = ± y . 

2 '^ 2 


a i/i + cos a 

cos - — ± y — , 

2 2 


a ,/i — cos Of 

tan - = ± y — . 

2 I + cos a 


sin a I — cos a 


I + cos a sin or ' 



TRIGONOMETRIC FORMULA. 27 

Functions of Two Angles, a and (3. 

sin {a ± /i) = sin a cos /i ± cos a sin (3. 

cos {(X ± /i) = cos a cos /? =F sin a; sin /?. 

.^ / , /?v tan rt- ± tan ft 

tan (rt' ± p) = '—-, 

^ ' ' I T tan ar tan yS 

, ^, cot « cot /? q: I 

cot (a±B)-= '- . 

^ ' ' cot /i ± cot a 

sin {a -^ ft) A- sin(rt' — y^) = 2 sin « cos ft. 
sin («+/?) — sin(a' — ft) — 2 cos «r sin ft. 
cos (^ — ^) + cos(r»' + /?) = 2 cos or cos ft. 
cos (of — /5) — cos(a + /?) = 2 sin a sin /5. 
sin a + sin /? = 2 sin |(ar 4- ft) cos |^(« — /?). 
sin a — sin /? = 2 cos |(cir + ft) sin i(ar — y5). 
cos /? + cos « = 2 cos 1(0' + ft) cos |(« — /J), 
cos ft—co?>a=2 sin i(ar + ft) sin ^(a — yS). 

, . o sinfa ± ft) 

tan a ± tan ft = ^^ — —-^. 

cos a cos p 

4. /? r ^ sin(a' ± /?) 

cot ft ± cot a = ^— ^^ -—:. 

sin a sin p 

sin or -|- sin y5 _ tan l(a + y5) 
sin a — sin yS tan ^{a — /?) ' 

sin a + sin y3 _ sin(a' — ft) 
sin(ar + /i) sin « — sin /?* 

cos ft 4- cos ex , ^s , 

^ = cot J (a- + ft) cot 4(« - ft). 

cos p — COS a -V I / / j\ /-/ 

tan a -\- tan /g _ cot ft + cot ar _ sin (a + /?) 
tan a — tan /? cot ft — cot or ~ sin [a — ft)' 



TRIGONOMETRIC FORMULAE. 



Developments of Trigonometric Functions. 

Sin = — f^ + r- — r-+etc. cos 0= i — f- + f- — ^+ etc. 

|3 |5_ \1_ |2 |4 |6_ 

0' 20' 170' 620' 

tan := 4- -^- + -^- + ^ + -f + etc. 
3 15 315 2835 

^10 0' 20' 0' 

cot0 = -7 — - — — ^ etc. 

3 45 945 4725 

, 0' , 50' 610" , 13850' , 

sec = I + ^ + ^- + -^ + -^^- + etc. 

2 4 p 

^ I , , 70', 310' , 3810' , 
cosec = - + f- + ^- + ^— ^ + ^--^ + etc. 

|3 3|5. 3|l 5|9 

|« = 1 .2.3 «. U = 24. Is ~ ^^°' 1^ — 720- 

|7 = 5040. [8 = 40320. Ip = 3628S0. 

Powers of sin a and cos a, 

. » I — cos 2a » cos 20' + I 

sin a = . cos a = . 

2 2 

sin a — cos 2a sin a _ 3 sin a — sin ^a 



sin a = 



sin a 



2 4 

cos 2a cos or + cos a _ cos 30^-1-3 cos a 

2 ~ 4 
3 — 4 cos 2ar + cos 4a 



. cos 4a + 4 cos 20' + 3 

cos a = ■ ■ — . 



Relations between Parts of Plane Triangles. 

Notation, a, b and c denote sides, and A, B and C their re- 
spective opposite angles. A = area of triangle, a -\- b •\- c ^= s. 
A -\- B -\- C =^ S. y? = radius of circumscribed circle, r = radius 
of inscribed circle. 



TRIGONOMETRIC FORMULiE. 29 

Right Plane Triangles. C = 90". 

<i=^ c sin A. a ^^b tan A. 

b = c COS A. b = a cot A. 

c'^a^j^ b\ A = ^-. 

2 



Oblique Plane Triangles. 
^l = ^-£smA= Vy{is-a){is-b){y-e) =f^='f 



sin A sin jB sin C* 

« + ^ : a — <^ : : tan ^(A + ^) : tan ^{A — £). 



,0S ^ = '' + '-"'. COS i^ = f'Mii^'L). 



,i„ ^^ = ^jy-ms-A, tan i^ ^ ^i^-ms-c) 

^ ^ be - r Hi^-«) 

Relations between Parts of Trihedrals. 

Notation, or, ^ and ^ denote face-angles, and A, B and C 
their respective opposite dihedrals. 



Right Trihedrals. A = 90°, 

cos a = cos /? cos ^. cos a = cot ^ cot C. 

sin /? = sin a sin ^. sin /? = tan y cot C 

sin y =■ sin « sin C. sin ;/ = tan ft cot -5. 

cos B = cos yS sin C. cos ^ = cot a tan ;'. 

cos C = cos y sin ^. cos C = cot or tan /?. 



3© TRIGONOMETRIC FORMUL/E. 



Oblique Trihedrals. 



sin a _ sin (3 _ sin y 
sin A sin B sin C' 



cos a = cos /? cos y -)- sin /? sin y cos y^. 
cos ^ = — cos B cos C+ sin B sin C cos a, 
cot a sin ;/ = cos y cos ^ + sin B cot ^. 

sin M = j/ sin(i^ - /^) sin(^^ - y) ^ 
^ ^ sin /i^ sin y 

. . i/sin \s sin(4i' — a) 

cos \A — y \ — -^ '. 

"^ sin p sin y 

tan l^ = y^53EE2SEZ3. 
"^ ' sin ^^ sin(^j — a) 

. . ./ — cos i-S'cosfi^'— ^) 
''"i^^y sin £ sin C ■• 

** '^ sin ^ sin 6 

_ i / — cos ^6" cos(^6' — A) 
tan -^a-y cos^^- - ^) cos(i6'-Cy 

Napier's Analogies. 
cos ^(ar + /?) : cos ^(a -/?):: cot \C : tan ^(^ + ^). 
sin Ua + /?) : sin l-{a — /3) :: cot ^C : tan ^{A - B). 
cos ^{A + ^) : cos ^{A - B) :: tan i>/ : tan ^{a + yS). 
sin ^{A + ^) : sin h{A - B) :: tan i^ = tan ^{a - /?). 



TRIGONOMETRIC FORMULAE. 3I 



Spherical Triangles, 

Notation, a, b and c denote sides subtending face-angles a, 
/Sand y, respectively, of the corresponding trihedral. A, B and 
C denote their respective opposite dihedrals. E = spherical 
excess of triangle in radians. J = area of trjangle. J^ = radius 
of sphere. 

a = Ra. b = Rft. c = Ry. 

^= -^(^ + ^+C- 180°). A = ER\ 

loO 



When a, b, c and R are given, E may be computed directly 
from the face-angles a, f3 and y, by the formula 

tan IE = 4/tan ^s tan ^{^s — a) tan ^{^ — /3) tan ^{y — y). 









TABLE I. 






Common, or Briggs', 




i 


[.OGARIIHMS OF .S UMBERS. 








iHROM 1 xo 11009. 






I 


Log. 


N. 


Log. 


N. 


Log. 


N. 


Log. 


N. 


Log. 


— 00 


20 

21 


1.30 103 


40 

41 


1.60 206 


60 

61 


i^77 815 


80 
81 


1.90 309 


0.00 000 


1.32 222 


I. 61 278 


^•78 533 


1.90 848 


2 


.30 103 


22 


•34 242 


42 


.62 325 


62 


•79 239 


82 


.91 381 


3 


•47 712 


23 


•36 173 


43 


'63 347 


63 


•79 934 


83 


.91 908 


4 


0.60 206 


24 


1.38 021 


44 


1^64 345 


64 


1.80 618 


84 


1.92 428 


5 


.69 897 


25 


.39 794 


45 


•65 321 


65 


.81 291 


85 


.92 942 


6 


.77 815 


26 


.41 497 


46 


.66 276 


66 


.81 954 


86 


.93 450 


7 


0.84 510 


27 


1-43 136 


47 


1.67 210 


67 


1.82 607 


87 


^•93 952 


8 


.90 309 


28 


•44 716 


48 


.68 124 


68 


•83 251 


88 


•94 448 


9 
10 

II 


.95 424 


29 
30 

31 


.46 240 


49 
60 

51 


.69 C19 


69 
70 
71 


•83 885 


89 
90 

91 


•94 939 


I. 00 000 


1.47 712 


I .69 897 


1.84 510 


1.95 424 


1.04 139 


1.49 136 


1.70 757 


1.85 126 


1.95 904 


12 


.07 918 


32 


•50 5^5 


52 


.71 600 


72 


•85 733 


92 


.96 379 


13 


.11 394 


33 


.51 851 


53 


.72 427 


73 


.86 332 


93 


.96 848 


14 


I. 14 613 


34 


^•53 148 


54 


1^73 239 


74 


1.86 923 


94 


1-97 3^3 


15 


.17 609 


35 


•54 407 


55 


•74 036 


75 


.87 506 


95 


•97 772 


i6 


.20 412 


36 


•55 630 


56 


•74 819 


76 


.88 081 


96 


.98 227 , 


17 


1.23 045 


37 


1.56 820 


57 


1^75 587 


77 


1.88 649 


97 


1.98 677 1 


i8 


.25 527 


38 


•57 978 


58 


•76 343 


78 


.89 209 


98 


.99 122 


19 
20 


.27 875 


39 
40 


•59 106 


59 
60 


•77 085 


79 
80 


.89 762 


99 
100 


•99 563^ 


1.30 103 


1.60 206 


1^77 815 


1.90 309 


2.00 000 


N. 


Log. 


N. 


Log. 


N. 


Log. 


N. 


Log 


N. 


Log. 



TABLE I. 



Tn." 





1 


2 


3 


4 


5 


6 


7 


8 


9 P. P. ll 


100 

lOI 
I02 


00 000 


043 


087 


130 


173 


216 


260 


303 


346 


389 


1 


432 
860 


475 
902 


518 
945 


561 
987 


604 
*03o 


646 

*072 


689 
*ii4 


732 
*i57 


775 
*i99 


817 
*24i 




43 43 42 41 


103 


01 283 


326 


368 


410 


452 


494 


536 


578 


619 


661 


.2 


8.7 


8.6 


8.4 


8.2 


104 


703 


745 


787 


82s 


870 


911 


953 


994 


*o36 


*o77 


• 3 


13.0 


12.9 




•2-3, 


!ios 


02 1 19 


160 


201 


243 


284 


325 


3(^6 


407 


448 


4S9 


•4 


17.4 

21.7 


17.2 
21.5 


16.8 
21.0 


16. 4! 

20. s 1 


106 


530 


571 


612 


653 


694 


735 


775 


816 


857 


898 


.6 


26.1 


25.8 


25.2 


24.6 


107 


938 


979 


*oi9 


*o6o 


*io5 


*i4i 


*i8i 


*22I 


*262 


*302 


•7 


30-4 


30.1 


29.4 


28.7 


108 


03 342 


382 


422 


463 


503 


543 


583 


623 


663 


703 


■9 


34.8 

39.1 


34-4 
38.7 


33-lJ 
.37-8 


32.8 
36-9 


109 
110 

III 
112 


742 


782 


822 


862 


901 


941 


981 


020 


060 


100 




04 139 


178 


218 


257 


297 


336 


375 


415 


454 


493 


532 
922 


571 
960 


616 
999 


649 

*038 


688 
*o76 


727 
*ii5 


766 
*i54 


805 
*I92 


844 

*23I 


883 
*269 


.1 


46 

4.0 


40 

4.0 


39 38 

3-9| 3-8 


113 


05 308 


346 


384 


423 


461 


499 


538 


576 


614 


652 


.2 


8.1 


8.0 


7.8 


7.6 


114 


6go 


728 


766 


804 


842 


880 


918 


956 


994 


*032 












115 


06 070 


107 


145 


^83 


220 


258 


296 


333 


371 


408 


•4 

■S 


20.2 


20.0 


15.0 
19 ..s 


15-2 

19.0 


116 


446 


483 


520 


558 


595 


632 


670 


707 


744 


781 


.6 


243 


24.0 


23-4 


22.8 


117 

118 


818 
07 188 


855 
225 


893 
261 


930 

298 


967 

335 


*oo4 
372 


*o4o 
408 


*o77 
445 


*iX4 
481 


*i5i 
518 


•7 
.8 
•9 


28.3 
32-4 
36.4 


28.0 
32.0 
36.0 


27-3 
31-2 
35-1 


26.6 
30.4 
34.2 


119 
120 
121 


554 


591 


627 


664 


700 


737 


773 


809 


845 


882 




918 


954 


990 


*026 


*o62 


*098 


*i34 


*i76 


*206 


*242 


o§ 278 


314 


350 


386 


422 


457 


493 


529 


564 


606 


122 


636 


671 


707 


742 


778 


813 


849 


884 


920 


955 




0/ 


0/ 


0^ OD 1 

6' ^ <^ II 


123 


990 


*026 


*o6i 


*096 


*i3i 


*i66 


*202 


*237 


*272 


'^'307 


,2 


7-5 


7-4 


7.2 
10.8 


7.0 


124 


09 342 


377 


412 


447 


482 


517 


552 


586 


621 


656 


•i 






10.5 


125 


691 


725 


760 


795 


830 


864 


899 


933 


968 


*002 


•4 
•S 


150 
18.7 


18. s 


14.4 
18.0 


14.0 

17. s 


126 


10 037 


071 


106 


140 


174 


209 


243 


277 


312 


346 


.6 


22.5 


22.2 


21.6 


21.0 


127 


380 


414 


448 


483 


517 


551 


S8S 


619 


653 


687 


■7 


26.2 


25.9 


25.2 


24.5 


128 


721 


755 


789 


822 


856 


890 


924 


958 


991 


*025 


•9 


30.0 

33-7 


33-3 


32-4 


31-5 


129 
130 

131 


II 059 


092 


126 


160 


193 


227 


266 


294 


327 


361 




394 


427 


461 


494 


528 


561 


594 


627 


661 


694 


727 


766 


793 


826 


8S9 


892 


925 


958 


991 


*024 


132 


12 057 


090 


123 


156 


189 


221 


254 


287 


320 


352 


34 34 33 32 


133 


385 


418 


450 


483 


515 


548 


580 


613 


645 


678 


.2 


3-4 
6.9 


3-4 

6.8 


3-3 
6.6 


6.4 1 


134 


716 


743 


775 


807 


840 


872 


904 


937 


969 


*OOI 


• 3 


10.3 


10.2 


9.9 


9.6 


135 


13 °33 


065 


097 


130 


162 


194 


226 


258 


290 


322 


■4 


'3-« 


I3-C 


132 


12.8 
16.0 


136 


354 


386 


417 


449 


481 


513 


545 


577 


608 


640 


.6 


20.7 


20.4 


19.8 


19.2 


137 


672 


703 


735 


767 


798 


830 


862 


893 


925 


956 


■7 


24.1 


238 


23.1 


22.4 


138 


988 


*oi9 


*o5i 


*o82 


*ii3 


*i45 


*i76 


*207 


*239 


*270 


.8 
•9 


27.6 
31.0 


27.2 
30.6 


26.4 
29.7 


25.6 
28.8 


139 
140 

141 

142 


14 301 


332 


364 


395 


426 


457 


488 


519 


550 


582 


1 


613 


644 


675 


706 


736 


767 


798 


829 


866 


891 


922 
15 229 


952 
259 


983 
290 


*oi4 
320 


*o45 
351 


*o75 
38 i 


*io6 
412 


*i37 

442 


*i67 
473 


*i98 
503 




31 


31 30 

,1 TO 


29 


M3 


533 


564 


594 


624 


655 


685 


715 


745 


776 


806 


.2 


6-3 


6:2 


6.0 


5.8 


144 


836 


866 


896 


926 


956 


987 


*oi7 


*o47 


*o77 


*io7 


■3 


9-4 


y-3 


y.o 


8.7 


145 


16 137 


166 


196 


226 


256 


286 


316 


346 


376 


405 


•4 

■ S 


15-7 


12.4 


12.0 

IS.O 


14.5 


146 


435 


465 


494 


524 


554 


584 


613 


643 


672 


702 


.6 


18.9 


18.6 


18.0 


17-4 


147 


731 


761 


791 


820 


849 


879 


908 


938 


967 


997 


•7 


22.0 


21.7 


21 .0 


20.3 


148 


17 026 


055 


085 


114 


143 


172 


202 


231 


260 


289 


•9 


25.2 
28.3 


27.9 


24.0 
27.0 


26.1 


149 
160 


318 


348 


377 


406 


435 


464 


493 


522 


551 


580 




609 


638 


667 


696 


725 


753 


782 


811 


840 


869 


N. 





1 


2 


3 


4 


6 


6 


7 


8 


9 


P.P. 



LOGARITHMS OF NUMBERS. 



N. 





1 12 


li 


4 


r> « 1 7 1 8 1 1 


p. i». 


150 

151 


17 609 


638 


667 


696 


725 


753 


782 


8ii 


840 


869 


2Q 28 5>'7 


897 


926 


955 


984 


*OI2 


*o4i 


*o7o 


*098 


*I27 


*i56 


152 


18 184 


213 


241 


270 


298 


327 


355 


384 


412 


440 






' 1 
2.8 a. 7 !l 


153 


469 


497 


526 


554 


582 


611 


639 


667 


695 


724 


.2 


S-8 


5.< 


' 5-4 


154 


752 


786 


808 


836 


864 


893 


921 


949 


977 


*oo5 










155 


19 033 


061 


089 


117 


145 


173 


201 


229 


256 


284 


4 

.5 


MS 


14. c 


)' 13.5 


i5<> 


312 


340 


368 


396 


423 


451 


479 


507 


534 


562 


,6 


17-4 


16. ( 


5 16.2 


157 


590 


617 


645 


673 


706 


728 


755 


783 


816 


838 


•7 


20.3 


iq.< 


5 18.9 


158 


865 


893 


920 


948 


975 


*oo3 


*o3o 


*o57 


*o85 


*i 12 


•9 


23.2 
26.1 


25- 


>j 21.6 
jI 24.3 


159 
160 

161 


20 139 


167 


194 


221 


249 


276 


303 


330 


357 


385 


-,? ^A 


412 


439 


466 


493 


526 


547 


574 


601 


628 


655 


6S2 


709 


736 


763 


796 


817 


844 


871 


898 


924 


162 


951 


978 


*oo5 


*032 


*o58 


*o85 


*II2 


*i39 


*i65 


♦192 




*o 


2.6 


ib3 


21 219 


245 


272 


298 


325 


352 


378 


405 


431 


458 


.2 


5-3 


5-2 


164 


484" 


511 


537 


564 


590 


616 


643 


669 


695 


722 


•3 


7-9 


7.8 


165 


748 


774 


801 


827 


853 


880 


906 


932 


958 


984 


■4 
.5 


to. 6 

13.2 


10 4 
13 


166 


22 01 1 


037 


063 


089 


115 


141 


167 


193 


219 


245 


.6 


15.9 


15.6 


!i67 


271 


297 


323 


349 


375 


401 


427 


453 


479 


505 


•7 


18.5 


18 2 


168 


531 


557 


582 


608 


634 


660 


686 


711 


737 


7(>3 


• 9 


23-8 


234 


i 169 

170 

I171 


788 


814 


840 


865 


891 


917 


942 


968 


994 


*oi9 


2S 25 24 


23 045 
299 


070 


096 


121 


147 


172 


198 


223 


249 


274 


325 


350 


375 


401 


426 


451 


477 


502 


527 


172 


553 


578 


603 


628 


653 


679 


704 


729 


754 


779 


173 


804 


829 


855 


880 


905 


930 


955 


980 


*oo5 


*o3o 


.2 


5-1 


5 


5 •'•4 
4.8 1 


! 174 


24055 


080 


105 


129 


154 


179 


204 


229 


254 


279 


•3 


7-6 


7- 


5 7-2 


175 


304 


328 


353 


378 


403 


427 


452 


477 


502 


526 


•4 


10.2 


10. 


9.6 


176 


551 


576 


600 


625 


650 


674 


699 


723 


748 


773 


.6 


'5-3 


15- 


14.4 


177 


797 


822 


846 


871 


895 


920 


944 


968 


993 


*oi7 


•7 


i7§ 


17- 


5 16.8 


178 


25 042 


065 


091 


115 


139 


164 


188 


212 


237 


261 


.8 
•9 


20.4 

22.5 


20. 

22. 


19.2 
■; 21.6 


179 

180 

181 
182 


285 


309 


334 


358 


382 


406 


430 


455 


479 


503 


23 23 


527 


551 575 


599 


623 


647 


672 


696 


720 


744 


768 
26 007 


792 
031 


816 
055 


840 
078 


863 
102 


887 

126 


911 

150 


935 
174 


959 
197 


983 
221 


183 


245 


269 


292 


316 


340 


3<^3 


387 


411 


434 


458 


.2 


4-7 


4.6 


184 


482 


505 


529 


552 


576 


599 


623 


648 


670 


693 


•3 


7.0 


6.9 


18S 


717 


740 


764 


787 


811 


834 


858 


881 


904 


928 


•4 


9-4 


9.2 


186 


951 


974 


998 


*02I 


*o44 


*o68 


*o9i 


*ii4 


*i37 


*i6i 


.6 


14. 1 


'3.8 


187 


27 184 


207 


230 


254 


277 


300 


323 


346 


369 


392 


•7 


16.4 


16. 1 


188 


416 


439 


462 


485 


508 


531 


554 


577 


600 


623 


• 9 


21. i 


18.4 
20.7 


189 
190 

191 


646 


669 


692 


715 


738 


761 


784 


806 


829 


852 




875 


898 


921 


944 


966 


989 


*OI2 


*o35 


*o58 


*o8o 


28 103 


126 


149 


171 


194 


217 


239 


262 


285 


307 


192 


330 


352 


375 


398 


420 


443 


465 


488 


510 


533 


22 22 21 


193 


555 


578 


600 


623 


645 


668 


690 


713 


735 


758 


.2 


4-5 


4- 


; Zsi 


194 


780 


802 


825 


847 


869 


892 


914 


936 


959 


981 


•3 


6.7 


b. 


6 6.4 


195 


29 003 


025 


048 


070 


092 


114 


137 


159 


181 


203 


■4 


9-9 


8. 


8 8.6 


196 


225 


248 


270 


292 


314 


336 


358 


380 


402 


424 


.6 


3-5 


13- 


2 12.9 


197 


446 


468 


490 


512 


534 


556 


578 


600 


622 


644 


• 7 


5-7 


'S-4 


15.0 


198 


666 


688 


710 


732 


754 


776 


798 


820 


841 


863 


.8 


8.0 


17.6 

TO 8 


17.2 


199 
200 


885 


907 


929 


950 


972 


994 


*oi6 


*o38 


*o59 


*o8r 




30 103 


124 


146 


168 


190 


211 


233 


254 


276 


298 


N. 





1 


2 


3 


4 


5 1 6 


7 


8 


9 


P. P. 



TABLE I. 



N. 
200 

20I 
202 
203 
204 
205 
206 
207 
208 
209 

210 

III 
212 
213 
214 

215 
216 

217 
218 
219 
220 

221 
222 
223 
224 
225 
226 
227 
228 
229 
230 
231 
232 
233 
234 
235 
236 

237 
238 

239 
240 

241 
242 
243 
244 

245 
246 

247 
248 
249 
250 



O 

30 103 

3^9 
535 
749 
963 

31 175 
386 

597 
806 

32 014 
222 
428" 

838 

33 041 

244 

445 
646 

845 

34 044 



242 



439 
635 

830 

35 025 

218 

411 
602 
793 
983. 

36 173 



361 
549 
735 
921 

37 107 
291 

475 
657 
840 



38 021 



201 

38! 
560 

739 

9^6 

39 093 

269 

445 
620 

794 
O 



124 



449 
654 
858 
061 
264 
465 
666 
865 
064 



262 



459 
655 
850 

044 
237 
430 
621 
812 
''002 



191 



380 

567 
754 
940 
125 
309 

493 
676 



039 



219 
399 
578 
757 
934 
III 

287 
462 
637 



146 



3^3 
578 
792 

'005 
217 
429 

639 
848 
056 



263 



469 
674 

878 
082 
284 
485 
686 
885 
084 



478 
674 
869 
063 
257 
449 
641 
83 f 



399 
586 

773 
958 
143 
328 

511 
694 

876 



057 



237 
417 
596 
774 
952 
129 

305 
480 

655 

828 

2 



168 



384" 

599 

813 

''027 

239 
450 
660 
869 
077 
284 



490 

695 
899 

102 

304 
505 
706 

905 
104 



301 



498 
694 

889 

083 
276 
468 
660 

850 
'046 



229 



075 



255 
435 
614 

792 
970 
146 
322 

497 
672 

"846" 



190 



406 
621 

835 
*048 
260 
471 
681 
890 
097 



304 



510 
715 
919 

122 
324 
525 
726 

925 
123 



321 



5^8 
713 
908 
102 

295 
487 
679 
869 

'059 



436 
623 
810 
996 

180 
364 

548 

730 
912 



093 



273 
453 
632 

810 
987 
164 

340 

515 

689 



427 

642 

856 
*o69 
281 
492 
702 
910 
118 



325 

531 
736 
940 

142 

344 
546 
746 

945 
143 



341 



537 
733 
928 

121 
314 
507 
698 

888 
'o78 



267 



455 
642 

828 

'014 

199 

383 

566 

749 

930 

III 



291 

471 
650 

828 

'005 

i8i 

357 
532 
707 




557 
752 
947 
141 

334 
526 

717 
907 
'097 



286 



474 
661 
847 

'033 
217 
401 

584 
767 

948 



129 



309 
489 
667 

845 
'023 

199 

375 
550 
724 
898 

6 



576 
772 
966 
160 
353 
545 
736 
926 
*ii6 



305 



492 
679 
866 
^051 
236 
420 
603 

785 
967 



147 



327 
507 
685 

863 
'040 
217 

392 
567 

742 

915 



596 
791 
986 
179 
372 
564 

755 
945 
'135 



323 



511 
698 
884 

''070 
254 
438 
621 
803 
985 



165 



345 
525 
703 
881 
*o58 
234 
410 
585 
759 
933 
8 



1^1 
363 
543 
721 

899 

*o76 
252 

427 
602 

776 
950 
9 



P. P. 





22 


.1 


2.2 


.2 


4.4 


•3 


6.6 


•4 


8.8 


■S 


II. 


.6 


132 


• 7 


15-4 


.8 


17.6 


•9 


19.8 



20 

2.6 

4.1 

6.1 

8.2 
10.2 
12.3 

14-3 
16.4 
18.4 





19 


.1 


1.9 


.2 

•3 


3-9 

5-8 


•4 

■ 5 


7.8 
9-7 


.6 


II. 7 


•7 


13-6 


.8 


iS-b 


•9 


17-5 



18 



.1 


1-8 


.2 

•3 


3-7 
5-5 


•4 

•5 


7.4 
q.2 


.6 


II. I 


•7 


12.9 


.8 


14.8 


•9 


16.6 



17 



.1 


1-7 


.2 

■3 


3-5 

5-2 


• 4 


7.0 


•5 


8.7 


.6 


10.5 


.7 


12.2 


.8 
•9 


14.0 

15-7 



P.P. 



LOGARITHMS OF NUMBERS. 



1 N. 





1 1 2 


;? 1 4 


5 


« 1 7 1 8 i i» 1 


l». I\ 


250 

251 


39 794 


811 1 823 


846 


863 


881 


898 


915 


933 950 




967 


984 


*002 


*oi9 


*036 


*o54 


*o7i 


*o88 


*io5 


*I23 


1252 


40 140 


157 


174 


191 


209 


226 


243 


260 


277 


295 




{253 


312 


329 


346 


3(^3 


380 


398 


415 


432 


449 


466 




17 


17 


254 


483 


500 


517 


534 


551 


569 


586 


603 


620 


637 


. I 
.2 


1-7 

"1 . '^ 


1-7 

T .J. 


255 


654 


671 


688 


705 


722 


739 


756 


773 


790 


807 


■ ^ 


5-2 


5-1 


256 


824 


841 


858 


875 


892 


908 


925 


942 


959 


976 








257 


993 


*OIO 


*027 


*044 


*o6i 


*o77 


*094 


*iii 


*I28 


*i45 


• 4 

. 5 


7.0 

8.7 


6.8 


258 


41 162 


179 


19^ 


212 


229 


246 


263 


279 


296 


313 


.6 


10.5 


10.2 


259 
260 

261 


33° 


346 


3(^3 


380 


397 


413 


430 


447 


464 


486 
647 


•7 

.8 

•9 


12.2 
14.0 

15-7 


II. 9 
13-6 
15-3 


497 


514 


530 


547 


564 


581 


597 


614 


631 


664 


680 


697 


714 


730 


747 


764 


780 


797 


813 


262 


830 


846 


863 


880 


896 


913 


929 


946 


962 


979 


1 


263 


995 


*OI2 


^023 


*o45 


*o6i 


*o78 


*094 


*ii I 


*I27 


*i44 




264 


42 160 


177 


193 


209 


226 


242 


259 


275 


292 


308 


rZ T/i 


265 


324 


341 


357 


373 


390 


406 


423 


439 


455 


472 






1.6 

3.2 


I266 


488 


504 


521 


537 


553 


569 


586 


602 


618 


635 


. I 
.2 


1-6 
3-3 


267 


651 


667 


683 


700 


716 


732 


748 


765 


781 


79? 


•3 


4.9 


4.8 


268 


813 


829 


846 


862 


878 


894 


910 


927 


943 


959 








269 
270 

271 


975 
43 ^36 


991 


*oo7 


*023 


*040 


^056 


*072 


*o88 


*io4 


*I25 


•4 
•5 
.6 


6.6 
8.2 
9.9 

11-5 
13.2 


6.4 
8.0 
9.6 


152 


163 


184 


200 


216 


233 


249 


265 

425 


281 


297 


3^3 


329 


345 


361 


377 


393 


409 


441 


272 


457 


473 


489 


505 


520 


53(S 


552 


5^8 


584 


606 


S 


12.8 1 


273 


616 


632 


648 


664 


680 


695 


711 


727 


743 


759 


■9 


14-8 


14.4 


1274 


775 


791 


8og 


822 


838 


854 


870 


886 


901 


917 




1275 


933 


949 


965 


980 


996 


*OI2 


*028 


*o43 


*o59 


*o75 




276 


44091 


105 


122 


138 


154 


169 


185 


201 


216 


232 


tP Tf 


277 


248 


263 


279 


295 


310 


326 


342 


357 


373 


389 




'J 


'^j 


278 


404 


420 


43.? 


451 


467 


482 


498 


513 


529 


545 


.2 


1 • 5 
3.1 


1 • 5 
3.0 1 


279 
280 

281 


560 


576 


591 


607 


622 


638 


653 


669 


685 


700 


• 3 

• 4 

•5 


4-6 

6.2 

7-7 


4-5 

6.0 

7-5 


716 


731 


747 


762 778 


793 


809 


824 


839 


855 
*oo9 


870 


886 


901 


917 


932 


948 


963 


978 


994 


282 


45 025 


040 


055 


071 


086 


102 


117 


132 


148 


163 


.6 


9-3 


9.0 


283 


178 


194 


209 


224 


240 


255 


270 


286 


301 


316 


.7 


10. § 


10.5 


284 


332 


347 


362 


377 


393 


408 


423 


438 


454 


469 


.8 


12.4 


12.0 


285 


484 


499 


515 


530 


545 


560 


576 


591 


606 


621 


•9 


13-9 


13-5 i 


286 


636 


652 


667 


682 


697 


712 


72f 


743 


758 


773 




287 


788 


803 


8i,S 


833 


84s 


864 


879 


894 


909 


924 




288 


939 


954 


969 


984 


999 


*oi4 


*029 


*o44 


*o59 


*o75 




289 
290 
291 


46 090 


105 


120 


135 


150 


165 


180 


195 


210 


225 


.1 
.2 

•3 


1.4 
2.9 
4-3 


2.8 , 

4.2 


240 


255 


269 


284 


299 


314 


329 


344 


359 


374 
523 


389 


404 


419 


434 


449 


464 


479 


493 


508 


292 


538 


553 


568 


583 


597 


612 


627 


642 


657 


672 


A 


•^.s 


■^ 6 


I 293 


687 


701 


716 


731 


746 


761 


77^ 


790 


805 


820 


■S 


7.2 


7.0 


294 


834 


849 


864 


879 


894 


903 


923 


938 


952 


967 


.6 


8.7 


8.4 


295 


982 


997 


*oii 


*026 


*o4i 


*o55 


*o76 


*o85 


*IOO 


*i 14 


. 7 


10. 1 


9.8 


296 


47 129 


144 


158 


173 


188 


202 


217 


232 


246 


261 


.8 


II. 6 


II. 2 


297 


27g 


296 


305 


319 


334 


348 


3^3 


378 


392 


407 


•9 


13-0 


12.6 


298 


421 


436 


451 


465 


480 


494 


509 


523 


538 


552 


: 


299 
300 


567 


5Si 


596 


610 


625 


639 


654 


668 


683 


697 


i 


712 


726 


741 


755 


770 


784 


799 


813 


828 


842 


IN. 


j 1 


2 


3 


4 


5 1 6 


7 


8 1 9 


p.p. 



TABLE I. 



! N. 





1 "1 


2 


3 


4 


6 


6 


7 1 8 


9 


P. P. 


300 

1301 


47 712 


726 


741 


755 


770 


784 


799 


813 


828 


842 
"986" 




856 


871 


885 


900 


914 


928 


943 


957 


972 


302 


48 000 


015 


029 


044 


058 


072 


087 


lOI 


"5 


130 




303 


144 


158 


173 


187 


201 


216 


230 


244 


259 


273 




304 


287 


301 


316 


330 


344 


358 


373 


387 


401 


415 




305 


430 


444 


458 


472 


487 


501 


515 


529 


543 


558 


^ 


306 


572 


586 


600 


614 


629 


643 


657 


671 


685 


699 




^4 


14 


307 


714 


728 


742 


756 


775 


784 


798 


812 


827 


841 


.2 


1.4 
2.9 


1.4 
2.8 


308 


855 


869 


883 


897 


911 


925 


939 


953 


967 


982 


•3 


4-3 


4.2 


309 
310 

311 


996 


*OIO 


*024 


*o38 


*052 


*o66 


*o8o 


*o94 


*io8 


*I22 


•4 
•5 
.6 


5.8 
7.2 
8.7 


5-6 
7.0 

8.4 


49 136 


150 


164 


178 


192 


206 


220 


234 


248 


262 


276 


290 


304 


3^8 


332 


346 


359 


373 


387 


401 


312 


415 


429 


443 


457 


471 


485 


499 


513 


526 


.540 




^ 


9.8 
II. 2 


3^3 


554 


5^8 


582 


596 


610 


624 


637 


65? 


665 


679 


•7 
.8 


II. 6 


3M 


693 


707 


720 


734 


748 


762 


776 


789 


803 


817 


•9 


I3-0 


12.6 


315 


831 


845 


858 


872 


886 


900 


913 


92^ 


941 


955 




316 


968 


982 


996 


*oio 


*023 


*o37 


*o5i 


*o65 


*o78 


*092 




317 


50 106 


119 


133 


147 


160 


174 


188 


201 


2 '5 


229 




31^ 


242 


256 


270 


283 


297 


311 


324 


338 


352 


365 




319 
320 

321 


379 


392 


405 


420 


433 


447 


463 


474 


488 ! 501 




515 


528 


542 


555 


569 


583 


596 


610 


623 1 637 


656 


664 


677 


691 


704 


718 


731 


745 


758 772 




1-3 
2.7 


•'J 

1-3 
2.6 


322 


785 


799 


812 


826 


839 


853 


866 


880 


893 


907 


.2 


323 


920 


933 


947 


960 


974 


987 


*OOI 


*oi4 


*02 7 


*o4i 


•3 


4.0 


3-9 


324 


51 054 


068 


081 


094 


108 


121 


135 


148 


161 


175 








325 


188 


201 


215 


228 


242 


255 


268 


282 


295 


30A 


•4 
.5 


5-4 
6.7 


5-2 

6.5 


326 


322 


335 


348 


361 


375 


388 


401 


415 


428 


441 


.6 


S.I 


7.8 


327 


455 


468 


48! 


494 


508 


521 


534 


547 


561 


574 




^ 




32« 


587 


6o5 


614 


627 


646 


653 


667 


680 


693 


706 


•7 
.8 


9.4 

10.8 


9.1 

10.4 


329 
330 

331 


719 


733 


746 


759 


772 


785 


798 


812 


825 


838 


•9 


12. i 


II. 7 


85 i 


864 


877 


891 


904 


917 


930 


943 


956 


969 




983 


996 


*oo9 


*022 


*o35 


*048 


*o6i 


*o74 


*o87 


*io6 


332 


52 114 


127 


140 


153 


166 


179 


192 


205 


218 


231 




i333 


244 


257 


270 


283 


296 


3°9 


322 


335 


348 


361 




334 


374 


387 


400 


413 


426 


439 


452 


465 


478 


491 




335 


504 


517 


530 


543 


556 


569 


582 


595 


608 


621 




336 


634 


647 


660 


672 


685 


698 


711 


724 


737 


750 




i^ 


1^ 


337 


763 


776 


789 


801 


814 


827 


840 


853 


866 


879 





2.5 


2.4 


33^ 


891 


904 


917 


930 


943 


956 


9^8 


981 


994 


*oo7 


•3 


3.7 


3.6 


339 
340 

341 


53 020 


033 


045 


058 


071 


084 


097 


109 


122 


135 


•4 
.5 
.6 


5-0 
6.2 
7-5 


4.8 
6.0 
7.2 


148 


160 


173 


186 


199 


211 


224 


237 


250 


262 


275 


288 


301 


3^-3 


326 


339 


352 


364 


377 


390 


342 


402 


415 


428 


440 


453 


466 


478 


491 


504 


516 


■7 

.8 


8.7 
10. 


8.4 
9.6 


343 


529 


542 


554 


567 


580 


592 


605 


618 


630 


643 


344 


656 


668 


681 


693 


706 


719 


731 


744 


756 


769 


•9 


II. 2 


10.8 


345 


782 


794 


807 


819 


832 


845 


857 


870 


882 


895 




346 


907 


920 


932 


945 


958 


970 


983 


995 


*oo8 


*020 




347 


54033 


045 


058 


070 


083 


095 


108 


126 


^33 


145 




34« 


158 


170 


183 


19s 


208 


220 


232 


245 


257 


270 




349 
350 


282 


295 


307 


320 


332 


344 


357 


369 


382 


394 




407 


419 


431 


444 


456 


469 


481 


493 


506 518 


N. 





1 


2 


3 


4 


5 


6 


7 


8 9 P.P. 1 



LOGARITHMS OF NUMRERS. 



N. 
350 





1 12 


;? 


4 


i* 


a 7 i s i 1 


■ > 


1*. 


54 407 


419 


431 


444 


456 


469 


481 


493 


506 


5^8 


. I 


12 
1 . 2 


530 


543 


555 


568 


580 


592 


605 


617 


629 


642 


.IS 2 


654 


666 


679 


691 


703 


716 


728 


740 


753 


765 


.2 


2.5 


353 


777 


790 


802 


814 


826 


839 


851 


863 


876 


888 


•3 


3-7 


354 


900 


912 


925 


937 


949 


961 


974 


986 


998 


*oi6 


•4 

.5 


5-9 1 

6.2 


355 


55 023 


035 


047 


059 


071 


0S4 


096 


log 


120 


133 


356 


145 


157 


169 


181 


194 


206 


218 


230 


242 


254 


.6 


7-5 ! 


[357 


267 


279 


291 


303 


315 


327 


340 


352 


364 


376 


• 7 

.8 


1 
8.7 
10. 


i35S 


388 


400 


412 


424 


437 


449 


461 


473 


485 


497 


|359 
360 

361 


509 


521 


533 


545 


558 


570 


582 


594 


606 


618 


•9 
. I 


II. 2 

12 

1.2 


630 


642 


654 


666 


678 


690 


702 


714 


726 


738 


750 


762 


775 


787 


799 


811 


823 


835 


847 


859 


362 


871 


883 


895 


907 


919 


931 


943 


955 


966 


978 


.2 


2.4 ; 


363 


990 


*002 


*oi4 


*026 


*o38 


*o5o 


*o62 


*o74 


*o86 


^098 


•3 


3.6 1 


1364 


56 no 


122 


134 


146 


158 


170 


181 


193 


205 


217 


• 4 

.5 


4-8 I 
6.0 1 


365 


229 


241 


253 


265 


277 


288 


300 


312 


324 


33(^ 


366 


348 


360 


372 


383 


395 


407 


419 


431 


443 


455 


.6 


7.2 1 


367 


466 


478 


490 


502 


514 


525 


537 


549 


561 


573 




8.4 i 
9.6 


368 


585 


596 


608 


620 


632 


643 


655 


667 


679 


691 


.8 


369 
370 

371 


702 


714 


726 


738 


749 


761 


773 


785 


796 


808 


•9 


10.8 
If 


820 


832 


843 


855" 


867 


879 


890 


902 


914 


925 


937 


949 


961 


972 


984 


996 


*oo7 


*oi9 


*o3i 


*042 


372 


57 054 


066 


077 


089 


lOI 


112 


124 


136 


147 


159 


.2 


2.3 ! 


373 


171 


182 


194 


206 


217 


229 


240 


252 


264 


275 


•3 


3-4 


374 


287 


299 


310 


322 


333 


345 


357 


368 


380 


391 




A f\ 


375 


403 


414 


426 


438 


449 


461 


472 


484 


495 


507 


.5 


■i.V i 


370 


519 


530 


542 


553 


565 


576 


588 


599 


611 


622 


.6 


6.9 j 


377 


634 


645 


657 


668 


680 


691 


703 


714 


726 


737 




8.0 

9.2 

10.3 

II 


37« 


749 


760 


772 


783 


795 


806 


818 


829 


841 


852 


•7 
8 


379 
380 

381 


864 


875" 


887 


898 


909 


921 


932 


944 


955 


967 


•9 


978 


990 


*OOI 


*OI2 


*024 


*o35 


*o47 


*o58 


^069 


*o8i 


58 092 


104 


115 


126 


138 


149 


161 


172 


183 


195 


382 


205 


217 


229 


240 


252 


263 


274 


286 


297 


308 


.2 


2.2 


3>i3 


320 


33^ 


342 


354 


365 


376 


-388 


399 


410 


422 


•3 


3-3 


384 


433 


444 


455 


467 


478 


489 


501 


512 


523 


535 






385 


546 


557 


568 


580 


591 


602 


613 


625 


636 


647 


•4 

•5 
.6 


4.4 

5-5 
6.6 


386 


658 


670 


681 


692 


703 


715 


726 


737 


748 


760 


387 


771 


782 


793 


804 


816 


827 


838 


849 


861 


872 






388 


883 


894 


905 


916 


928 


939 


950 


961 


972 


984 


•7 


7-7 

s s 


389 
390 

391 


995 


*oo6 


*oi7 


*028 


*039 


*o5o 


*o62 


*o73 
184 


*o84 


*o95 
206 


•9 


9 9 
Id 


59 ro6 


117 


128 


140 


151 


162 


173 


195 


217 


229 


240 


251 


262 


273 


284 


295 


306 


317 


392 


328 


339 


351 


362 


373 


384 


395 


406 


417 


428 


. I 


I .0 


393 


439 


450 


461 


472 


483 


494 


505 


516 


527 


538 


• 3 


3-1 


394 


549 


560 


571 


582 


593 


604 


615 


626 


637 


648 






'395 


659 


670 


681 


692 


703 


714 


725 


736 


747 


758 


•4 


4-2 


1396 


769 


780 


791 


802 


813 


824 


835 


846 


857 


868 


•5 
.6 


5-2 

6.3 


397 


879 


890 


901 


912 


923 


933 


944 


955 


968 


.977 






398 


988 


999 


*OIO 


*02I 


*032 


*043 


*o53 


*o64 


*o75 


^086 


•7 


7-3 
8.4 
9.4 i 


399 
400 


60 097 


108 


119 


130 


141 


151 162 


173 


184 


195 


.8 
•9 


206 


217 


227 


238 


249 


266 271 


282 


293 


303 





1 


2 


3 


4 


5 1 6 


7 


8 


9 


P 


P- 













TABLE 


: I. 












400 

401 





1 1 


fj 


1 3 


4 


5 


6 


7 


8 


9 


P 


• P. 


60 206 


217 


227 


238 


249 


260 


271 


282 


293 


303 






314 


325 


336 


347 


357 


368 


379 


39° 


401 


412 


402 


422 


433 


444 


455 


466 


476 


487" 


498 


509 


519 






403 


530 


541 


552 


563 


573 


584 


595 


606 


616 


627 






404 


638 


649 


659 


670 


681 


692 


702 


713 


724 


735 


.2 


2.2 


405 


745 


756 


767 


777 


788 


799 


810 


820 


831 


842 


•3 


3-3 


406 


852 


863 


874 


884 


895 


906 


916 


927 


938 


949 






407 


959 


970 


981 


991 


*00 2 


*oi3 


*023 


*o34 


*044 


*o55 


•4 

.5 


4.4 

5-5 


408 


61 066 


076 


087 


098 


log 


119 


130 


140 


151 


161 


.6 


6.6 


409 
410 

411 


172 


183 


193 


204 


215 


225 


236 


246 


257 


268 


• 7 

.8 

•9 


7-7 
8.8 
9.9 


278 


289 


299 


310 


320 


331 


342 


352 


363 


373 


384 


394 


405 


416 


426 


437 


447 


458 


468 


479 


412 


489 


500 


511 


521 


532 


542 


553 


563 


574 


584 






413 


595 


605 


616 


625 


637 


647 


658 


668 


679 


689 






414 


700 


710 


721 


731 


742 


752 


763 


773 


784 


794 




10 


415 


805 


815 


825 


836 


846 


857 


867 


878 


888 


899 


, I 


I 


416 


909 


920 


930 


940 


951 


961 


972 


982 


993 


*oo3 


.2 


2.1 


417 


62 013 


024 


034 


045 


055 


065 


076 


085 


097 


107 


•3 


3-1 


418 


117 


128 


138 


149 


159 


169 


180 


190 


200 


211 






419 
420 

j42I 


221 


232 


242 


252 


263 


273 


283 


294 


304 


314 


•4 
•5 
.6 

.7 


4.2 

5-2 

6.3 


325 


335 


345 


356 


366 


376 


387 


397 


407 


418 


428 


438 


449 


459 


469 


480 


490 


500 


510 


521 


422 


531 


541 


552 


562 


572 


582 


593 


603 


613 


624 


.8 


8.4 


423 


634 


644 


654 


665 


675 


685 


695 


706 


716 


726 


•9 


9.4 


424 


736 


747 


757 


767 


777 


788 


798 


808 


818 


828 






425 


839 


849 


859 


869 


879 


890 


900 


910 


920 


931 






426 


941 


951 


961 


971 


981 


992 


*002 


*OI2 


*022 


*032 




10 


427 


^3 043 


053 


063 


073 


083 


093 


104 


114 


124 


134 




428 


144 


154 


164 


175 


185 


195 


205 


215 


225 


235 


.2 


2.0 


429 
430 

431 


245 


256 


266 


276 


286 


296 


3O6 


3I6 


326 


336 


•3 

•4 
.5 


3-0 

4.0 
5-0 


347 


357 


367 


377 


387 


397 


407 


417 


427 


437 
538 


447 


458 


468 


478 


488 


498 


508 


518 


528 


432 


548 


558 


568 


578 


588 


598 


60s 


618 


628 


639 


.6 


6.0 


433 


649 


659 


669 


679 


689 


699 


709 


719 


729 


739 




7.0 
8.0 


434 


749 


759 


769 


779 


789 


799 


809 


819 


829 


839 


.8 


435 


849 


859 


869 


879 


889 


899 


909 


919 


928 


938 


•9 


9.0 


436 


948 


958 


968 


978 


988 


998 


*oo8 


*oi8 


*028 


*038 






437 


64 048 


058 


068 


078 


088 


098 


107 


117 


127 


137 






I43« 


147 


157 


167 


177 


187 


197 


207 


217 


226 


236 






439 
440 

441 


246 


256 


266 


276 


286 


296 


306 


315 


325 


335 


.1 
.2 
•3 


9 

0.9 
1.9 
2.8 


345 
444 


355 


365 


375 


384 


394 


404 


414 


424 


434 


453 


463 


473 


483 


493 


503 


512 


522 


532 


'442 


542 


552 


562 


571 


58? 


591 


601 


611 


621 


630 






443 


640 


650 


660 


670 


679 


689 


699 


709 


7I8 


728 


.4 


3-5 
4.7 


444 


738 


748 


758 


767 


777 


787 


797 


806 


Big 


826 


.6 


5.7 


445 


836 


846 


855 


865 


875 


885 


894 


904 


914 


923 






446 


933 


943 


953 


962 


972 


982 


992 


*OOI 


*OII 


*02I 


•7 
.8 


6.6 

7.6 


447 


65 031 


040 


050 


060 


069 


079 


089 


098 


108 


118 


•9 


8.5 


448 


128 


137 


147 


157 


166 


176 


186 


195 


205 


215 






449 
450 


224 


234 


244 


253 


263 


273 


282 


292 


302 


311 






321 


33^ 


340 


350 


360 


369 


379 


389 


398 


408 


N. 





1 i 2 


3 


4 


5 1 6 


7 


8 


9 


P 


.P. 



LOGARITHMS OF NUMBERS. 



xr 





1 1 1 3 


;5 


4 


5 


<> 


7 8 1) 1 


P. 


P. 


450 
4SI 


65 3-i 


331 340 


350 


360 


369 


379 


3S9 


398 1 408 






417 


427 


437 


446 


456 


466 


475 


485 


494 


5°4 


1452 


514 


523 


533 


542 


552 


562 


571 


581 


590 


600 






:453 


610 


619 


629 


638 


648 


657 


667 


677 


686 


696 






454 


705 


715 


724 


734 


744 


753 


763 


772 


782 


791 


.2 


2.0 


455 


801 


810 


820 


830 


839 


849 


858 


868 


877 


887 


•3 


3-0 


4S6 


896 


906 


915 


925 


934 


944 


953 


9^Z 


972 


982 






457 


991 


*OOI 


*OIO 


*020 


*029 


*o39 


*048 


*o5S 


*o67 


*o77 


•4 
.5 


4.0 
5.0 


4S8 


66 083 


096 


105 


115 


124 


134 


143 


153 


162 


172 


.6 


6.0 


459 
460 

461 


iSi 


190 


200 


209 


219 


228 


238 


247 


257 


266 


•7 

.8 

•9 


7.0 
8.0 
9.0 


276 


2S5 


294 


304 


313 


323 


2,Z2 


342 


351 


366 


370 


379 


389 


398 


408 


417 


426 


436 


445 


455 


462 


464 


473 


483 


492 


502 


511 


520 


530 


539 


548 






463 


558 


567 


577 


586 


595 


605 


614 


623 


^ZZ 


642 






464 


652 


661 


670 


680 


689 


698 


708 


717 


726 


736 




9 


465 


745 


754 


764 


773 


782 


792 


801 


816 


820 


829 




466 


838 


848 


857 


866 


876 


885 


894 


904 


913 


922 


.2 


0.9 
1. 9 


467 


931 


941 


950 


959 


969 


978 


987 


996 


*oo6 


*oi5 


•3 


2.8 


468 


67 024 


034 


043 


052 


061 


071 


080 


089 


099 


108 




3-8 
4-7 

5-7 

6.6 
7.6 


469 
470 

471 


117 

210 
302 


^^6 


136 


145 


154 


163 


173 


182 


191 


200 


•4 
•5 
.6 

.7 

.8 


219 228 


237 


246 


256 


265 


274 


283 


293 


311 


320 


329 


339 


348 


357 


366 


376 


385 


472 


394 


403 


412 


422 


431 


440 


449 


458 


467 


477 


473 


486 


495 


504 


513 


523 


532 


541 


550 


559 


5(^8 


•9 


8.5 


474 


578 


587 


596 


605 


614 


623 


^ZZ 


642 


651 


660 






475 


669 


678 


687 


697 


706 


715 


724 


733 


742 


751 






476 


760 


770 


779 


788 


797 


806 


815 


824 


833 


842 






477 


852 


861 


870 


879 


888 


897 


906 


915 


924 


933 




9 


478 


943 


952 


961 


970 


979 


988 


997 


*oo6 


*oi5 


*024 


.2 


0.9 
1.8 


479 

4S0 
481 


68033 


042 


051 


060 


070 


079 


088 


097 


106 


"5 


• 3 

•4 

• 5 


2.7 

3.6 
4-5 


124 


^r:, 


142 


151 


160 


169 


178 


187 


196 


205 


214 


223 


232 


241 


250 


259 


26§ 


277 


285 


295 


482 


304 


313 


322 


ZZT- 


340 


349 


358 


367 


376 


385 


.6 


5-4 


483 


394 


403 


412 


421 


430 


439 


448 


457 


466 


475 


.7 

.8 


6.3 
7.2 


484 


484 


493 


502 


511 


520 


529 


538 


547 


556 


565 


48s 


574 


583 


592 


601 


610 


619 


628 


637 


646 


654 


•9 


8.1 


486 


663 


672 


681 


696 


699 


708 


717 


726 


735 


744 






487 


753 


762 


770 


779 


788 


797 


806 


815 


824 


^ZZ 






488 


842 


851 


860 


868 


877 


886 


895 


904 


913 


922 




s 


489 
490 

491 


93^ 


940 


948 


957 


966 


975 


984 


993 


*002 


*oi5 


.1 
.2 
•3 


8 

0.8 
1.7 

2.5 


69 019 


028 


037 


046 


055 


064 


073 


081 


090 


099 


io8 


117 


126 


134 


143 


152 


161 


170 


179 


187 


492 


196 


205 


214 


223 


232 


240 


249 


258 


267 


276 






493 


284 


293 


302 


311 


320 


328 


337 


346 


355 


3(54 


• 4 

• 5 


3-4 
4.2 


494 


372 


385 


390 


399 


408 


416 


425 


434 


443 


451 


.6 


5-1 


495 


460 


469 


478 


487 


495 


504 


513 


522 


530 


539 




^ 


496 


548 


557 


565 


574 


583 


592 


606 


609 


618 


627 


•7 
.8 


5-9 
6.8 


497 


635 


644 


653 


662 


670 


679 


688 


697 


705 


714 


•9 


7-6 


498 


723 


731 


740 


749 


758 


766 


775 


784 


792 


801 






499 
500 


810 


819 


827 


836 


845 


853 


862 


871 


879 


888 






897 


905 


914 


923 


931 


940 


949 


958 


966 


975 


N. 





1 


2 


3 


4 


5 1 6 


7 


8 


9 


P. 


P- 













TABLE 


I. 














500 





1 


a 


3 


4 


5 1 6 


7 ! 8 


9 


p 


P. 




69 897 


905 


914 


923 


931 


940 


949 


958 9^6 


975 








984 


992 


*OOI 


*OIO 


*oi8 


*027 


*o36 


*o44 


*o53 


*o6i 




502 


70 070 


079 


087 


096 


105 


113 


122 


131 


139 


148 









503 


157 


i(>S 


174 


182 


191 


200 


208 


217 


226 


234 


.1 


0.9 




504 


243 


251 


260 


269 


277 


286 


294 


303 


312 


320 


.2 


1.8 




505 


329 


337 


346 


355 


3(>3 


372 


380 


389 


398 


406 


•3 


2.7 




506 


415 


423 


432 


441 


449 


458 


4^6 


475 


483 


492 


.J. 


T.6 




507 


501 


509 


518 


526 


535 


543 


552 


560 


569 


578 


•5 


4-5 




508 


586 


595 


603 


612 


620 


629 


637 


646 


654 


663 


.6 


5-4 




509 
610 

511 


672 


680 


689 


697 


706 


714 


723 


731 


740 


748 


•7 
.8 

•9 


6-3 
7.2 

8.1 




757 


7^ 


774 


782 


791 


799 


808 


816 


825 


833 




842 


850 


859 


867 


876 


884 


893 


901 


910 


918 




512 


927 


935 


944 


952 


961 


969 


978 


986 


995 


*oo3 








5^3 


71 on 


020 


028 


037 


045 


054 


062 


071 


079 


088 








5M 


096 


105 


113 


121 


130 


138 


147 


155 


164 


172 




s 




515 


180 


189 


197 


206 


214 


223 


231 


239 


248 


256 




8 




516 


265 


273 


282 


290 


298 


307 


315 


324 


332 


340 


.2 


0.8 
1-7 




517 


349 


357 


S66 


374 


382 


39^ 


399 


408 


416 


424 


•3 


2.5 




5i« 


433 


441 


449 


458 


466 


475 


483 


491 


500 


508 








519 
520 

521 


516 


525 


533 


542 


550 


558 


567 


575 


583 


592 


•4 
•5 
.6 


3-4 
4.2 

5-1 




600 


603 


617 


625 


633 


642 


650 


659 


667 


675 




684 


692 


700 


709 


717 


725 


734 


742 


750 


758 




522 


767 


775 


783 


792 


800 


808 


817 


825 


833 


842 


•7 
.8 


5-9 
6.8 




523 


850 


858 


867 


875 


883 


891 


900 


908 


9^6 


925 


•9 


7-6 




524 


933 


941 


949 


958 


968 


974 


983 


991 


999 


*oo7 








525 


72 016 


024 


032 


040 


049 


057 


065 


074 


082 


090 








526 


098 


107 


115 


123 


131 


140 


148 


156 


164 


173 








527 


181 


189 


197 


206 


214 


222 


230 


238 


247 


255 




8 




528 


263 


271 


280 


288 


296 


304 


312 


321 


329 


337 


.1 


0.8 
I 6 




529 
530 

531 


345 


354 


362 


370 


378 


386 


395 


403 


411 


419 


•3 
.4 


2.4 

3-2 

4.0 




427 


436 


444 


452 


460 


468 476 


485 


493 


501 




509 


517 


526 


534 


542 


550 


558 


566 


575 


583 




532 


591 


599 


607 


615 


624 


632 


640 


648 


656 


664 


.6 


4.8 




533 


672 


681 


689 


697 


705 


713 


721 


729 


738 


746 








534 


754 


762 


770 


778 


786 


795 


803 


811 


819 


827 


•7 
8 


5-6 
6.4 

7.2 




535 


835 


843 


85 i 


859 


868 


876 


884 


892 


900 


9°S 


•9 




536 


916 


924 


932 


941 


949 


957 


965 


973 


981 


989 








537 


997 


*oo5 


*oi3 


*02I 


*o3o 


*o38 


*o46 


*o54 


*o62 


*o7o 








538 


73 078 


086 


094 


102 


no 


118 


126 


134 


143 


151 








539 
540 

541 


159 


167 


175 


183 


191 


199 


207 


215 


223 


231 


.1 
.2 
.3 


1 

0.7 

1-5 
2.2 




239 


247 


255 


263 


271 


279 


287* 


295 


303 


311 




319 


328 


336 


344 


352 


360 


368 


376 


384 


392 




542 


400 


408 


416 


424 


432 


440 


448 


456 


464 


472 








543 


480 


488 


496 


504 


512 


520 


528 


536 


544 


552 


• 4 


3-9 




544 


560 


568 


576 


584 


592 


600 


608 


615 


623 


63^^ 


•5 
.6 


3-7 

4.5 




545 


639 


647 


655 


663 


671 


679 


687 


695 


703 


711 








546 


719 


727 


735 


743 


751 


759 


767 


775 


783 


791 


• 7 


5-2 




547 


798 


806 


814 


822 


830 


838 


846 


854 


862 


870 


• Q 


6.7 




54B 


878 


886 


894 


902 


909 


917 


925 


933 


941 


949 








549 
650 


957 


965 


973 


981 


989 


997 


*oo4 


*OI2 


*020 


*028 








74 036 


044 


052 


060 


068 


075 


083 


091 


099 


107 




N. 





1 


2 


3 


4 


5 


6 


7 


8 1 9 


P 


.P. 





LOGARITHMS OF NUMBERS. 



550 

551 





1 1 3 


3 


4 


n 





7 


8 


9 


1» 


1». 


74036 


044 ! 052 


060 


068 


075 


083 


091 


099 


107 






115 


123 


131 


139 


146 


154 


162 


176 


178 


186 


bb-' 


194 


202 


209 


217 


225 


233 


241 


249 


257 


264 






553 


272 


280 


288 


296 


304 


312 


319 


327 


33^ 


343 






554 


351 


359 


3<^6 


374 


382 


390 


398 


406 


413 


421 






555 
556 


429 


437 


445 


453 


460 


4^8 


476 


484 


492 


499 






507 


515 


523 


531 


538 


546 


554 


562 


570 


577 




8 


557 


5S5 


593 


601 


609 


616 


624 


632 


640 


648 


655 


.1 


0.8 

T (S 


55S 


663 


671 


679 


687 


694 


702 


710 


718 


72s 


733 


.3 


2.4 


559 
5G0 

561 


741 


749 


756 


764 


772 


7S0 


788 


795 


803 


811 


•4 

•5 
.6 


3-2 

4.0 

4.8 


819 


826 


834 


842 


850 


857 


865 


873 


881 


888 


896 


904 


912 


919 


927 


935 


942 


950 


958 


966 


50J 


973 


981 


989 


997 


*oo4 


*OI2 


*020 


*027 


*o3S 


*o43 






5^3 


75 051 


058 


066 


074 


081 


089 


097 


105 


112 


120 


•7 


5-6 


5^4 


128 


135 


143 


151 


158 


166 


174 


182 


189 


197 


•9 


7.2 


5^5 


205 


212 


220 


228 


235 


243 


251 


258 


266 


274 






566 


281 


289 


297 


304 


312 


320 


327 


335 


343 


350 






5^7 


358 


366 


373 


3^"^ 


389 


396 


404 


412 


419 


427 






50S 

569 
570 

571 


435 


442 


450 


458 


465 


473 


480 


488 


496 


503 






511 


519 


526 


534 


541 


549 


557 


564 


572 


580 




f 


587 


595 


602 


610 


618 


625 


633 


641 


648 


656 


663 


671 


679 


686 


694 


701 


709 


717 


724 


732 


b/'-' 


739 


747 


755 


762 


770 


777 


785 


792 


8o5 


808 




0.7 


5 73 


815 


823 


836 


838 


846 


853 


861 


868 


876 


883 


.3 


2.2 


574 


891 


899 


906 


914 


921 


929 


936 


944 


Q5I 


959 






b'/b 


967 


974 


982 


989 


997 


*oo4 


*OI2 


*oi9 


*027 


*o34 


•4 


3-° 


570 


76 042 


050 


057 


065 


072 


oSo 


087 


095 


102 


no 


•5 
.6 


3-7 
4-5 


577 


117 


125 


132 


140 


147 


155 


162 


170 


178 


185 






o/S 


193 


200 


208 


215 


223 


230 


238 


245 


253 


260 


•7 
.8 

•9 


5-2 

6.0 
6.7 


3 79 
580 

5S1 


268 


275 


283 


290 


298 


305 


313 


320 


328 


335 


343 


350 


358 


365 


372 


380 


387 


395 


402 


410 


417 


425 


432 


440 


447 


455 


462 


470 


477 


485 


58-' 


492 


500 


507 


514 


522 


529 


537 


544 


S52 


559 






5'^3 


567 


574 


582 


589 


596 


604 


611 


619 


626 


634 






i5«4 


641 


648 


656 


663 


671 


678 


686 


693 


700 


708 






I585 


715 


723 


730 


738 


745 


752 


760 


767 


775 


782 






5S(j 


790 


797 


804 


812 


819 


827 


834 


841 


849 


856 




7 


5«7 
5 88 


864 
937 


871 
945 


878 
952 


886 
960 


893 
967 


901 

974 


908 
982 


915 
989 


923 

997 


930 
*oo4 


.1 

.2 
.3 


0.7 

1-4 
2.1 


589 
590 

591 


77 oil 


019 


026 


033 


041 


048 


055 


063 


070 


078 


•4 
• 5 
.6 


2.8 

3-5 
4.2 


085 


092 


100 


107 


114 


122 


129 


U6 


144 


151 


158 


166 


173 


181 


188 


195 


2C3 


210 


217 


225 


592 


232 


239 


247 


254 


261 


269 


276 


283 


291 


298 






593 


305 


3^3 


320 


327 


335 


342 


349 


356 


364 


371 


•7 

8 


4.9 
5-6 
6-3 


594 


378 


386 


393 


400 


408 


415 


422 


430 


437 


444 


•9 


595 


451 


459 


466 


473 


481 


488 


495 


503 


510 


517 






59^5 


524 


532 


539 


546 


554 


561 


568 


575 


583 


590 






597 


597 


604 


612 


619 


626 


634 


641 


648 


655 


667, 






598 


670 


677 


684 


692 


699 


706 


713 


721 


728 


735 






599 
600 

i ^• 


742 


750 


757 


764 


771 


779 


786 


793 


8o5 


808 






815 


822 


829 


837 


844 


85 i 


858 


866 


873 


880 





1 


2 


3 


4 


5 


6 


7 


8 


9 


P 


P. 













TABLE I. 












N. 





1 


2 


3 


4 


5 


6 17 18 


<> 


P 


P. 


600 

6oi 


77 815 


822 


829 


837 


844 


85 J 


858 


866 


873 


880 






887 


894 


902 


909 


916 


923 


931 


938 


945 


952 


602 


959 


967 


974 


981 


988 


995 


*oo3 


*OIO 


*oi7 


*024 






603 


78 031 


039 


046 


053 


066 


067 


075 


082 


089 


096 






604 


103 


III 


118 


125 


132 


139 


147 


154 


161 


168 






605 


175 


182 


190 


197 


204 


211 


218 


226 


233 


240 






606 


247 


254 


261 


269 


276 


283 


290 


297 


304 


311 




1 


607 


319 


3^-^ 


333 


340 


347 


354 


362 


369 


376 


383 


.1 
.2 


0.7 
I. 5 


608 


390 


397 


404 


412 


419 


426 


433 


440 


447 


454 


.3 


2.2 


609 
610 

611 


461 


469 


476 


483 


490 


497 


504 


511 


518 


526 


•4 

•5 
.6 


3.0 

3-7 
4-5 


533 


540 


547 


554 


56J 


568 


575 


583 


590 


597 


604 


611 


618 


625 


632 


639 


646 


654 


661 


668 


612 


675 


682 


689 


696 


703 


710 


717 


725 


732 


739 






Ms 


746 


753 


760 


767 


774 


781 


788 


795 


802 


810 


■ 7 
.8 


5-2 

6.0 


614 


817 


824 


831 


838 


845 


852 


859 


866 


873 


886 


•9 


6.7 


615 


887 


894 


901 


9°8 


915 


923 


930 


937 


944 


951 






616 


958 


965 


972 


979 


986 


993 


*ooo 


*oo7 


*oi4 


*02i 






617 


79 028 


035 


042 


049 


056 


063 


070 


078 


085 


092 






618 


099 


106 


113 


120 


127 


134 


141 


148 


155 


162 






619 

620 

621 


169 


176 


183 


190 


197 


204 


211 


218 


225 


232 




7 


239 


246 


253 


260 


267 


274 


281 


288 


295 


302 


309 


316 


323 


33° 


337 


344 


351 


358 


365 


372 


622 


379 


386 


393 


400 


407 


414 


421 


428 


435 


442 


.2 


0.7 
I .a. 


623 


449 


45<> 


462 


469 


476 


483 


490 


497 


504 


511 


•3 


2.1 


624 


518 


525 


532 


539 


546 


553 


560 


567 


574 


581 






625 


588 


595 


602 


609 


616 


622 


629 


636 


643 


656 


•4 
• 5 
.6 




626 


657 


664 


671 


678 


6S5 


692 


699 


706 


713 


720 


4.2 


627 


727 


733 


740 


747 


754 


761 


768 


775 


782 


789 






628 


796 


803 


810 


816 


823 


830 


837 


844 


85 i 


8s8 


•7 


4.9 
5-6 
6.3 


629 
630 

631 


865 


872 


879 


886 


892 


899 


9O6 


9^3 


920 


927 


•9 


934 


941 


948 


954 


961 


968 


975 


982 


989 


996 


80 003 


010 


oig 


023 


030 


037 


044 


051 


058 


065 


632 


071 


078 


085 


092 


099 


106 


113 


120 


126 


133 






\(^33 


140 


147 


154 


161 


168 


174 


181 


188 


195 


202 






634 


209 


216 


222 


229 


236 


243 


250 


257 


263 


276 






035 


277 


284 


291 


298 


304 


311 


318 


325 


332 


339 






636 


345 


352 


359 


366 


373 


3S0 


386 


393 


400 


407 




6 


637 


414 


421 


427 


434 


441 


448 


455 


461 


468 


475 


.1 
2 


0.6 

T 1 


638 


482 


489 


495 


502 


509 


516 


523 


529 


536 


543 


.3 


1.9 


\^39 
640 

641 


550 


557 


563 


570 


577 


584 


591 


597 


604 


611 


.4 
.6 


2.6 

3-2 

3-9 


618 


625 


63i 


638 


645 


652 


658 


665 


672 


679 


686 


692 


699 


706 


713 


719 


726 


733 


740 


746 


642 


753 


760 


767 


774 


780 


787 


794 


801 


807 


814 






1^43 


821 


828 


834 


841 


848 


855 


861 


868 


875 


882 


•7 
8 


4-5 

5-2 

5-8 


644 


888 


895 


902 


909 


915 


922 


929 


936 


942 


949 


•9 


t'45 


956 


962 


969 


976 


983 


989 


996 


*oo3 


*OTO 


*oi6 






646 


81 023 


030 


036 


043 


050 


057 


063 


070 


077 


083 






647 


090 


097 


104 


no 


117 


124 


130 


137 


144 


151 






648 


157 


164 


171 


177 


184 


191 


197 


204 


211 


218 






649 
650 


224 


231 


238 


244 


251 


258 


264 


271 


278 


284 






291 


298 


304 


311 


318 


324 


33"^ 


338 


345 


351 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


P. 


P. 



LOGARITHMS OF NUMBERS. 



X. 





1 


2 


3 


4 


ii 


« 


7 8 


1) 


P 


. P. 


GoO 

651 


81 291 


298 


304 


311 


?>^^ 


3-M 


331 


338 


345 


351 






35S 


365 


371 


378 


385 


391 


398 


405 


411 


418 


652 


4-'5 


431 


438 


444 


451 


458 


464 


471 


478 


484 






653 


491 


498 


504 


511 


5'8 


524 


531 


538 


544 


551 






654 


55S 


564 


571 


577 


584 


591 


597 


604 


611 


617 






655 


624 


631 


637 


644 


650 


657 


664 


670 


677 


684 






656 


690 


697 


703 


710 


717 


723 


730 


736 


743 


750 




7 


657 


756 


76,3 


770 


776 


783 


789 


796 


803 


809 


816 


.1 


0.7 


65S 


822 


829 


836 


842 


849 


855 


862 


869 


875 


882 


.2 


1-4 
2. 1 


t^59 
660 

661 


888 


895 


901 


908 


915 


921 


928 


934 


941 


948 


•4 

.5 
.6 


2.8 

3-5 
4.2 


954 


961 


967 


974 


980 


987 


994 


*ooo 


*oo7 


*oi3 


82 020 


025 


0?,?, 


040 


046 


053 


059 


066 


072 


079 


662 


086 


092 


099 


105 


112 


118 


125 


131 


138 


145 






663 


151 


158 


164 


171 


177 


184 


190 


197 


203 


210 


•7 
.8 

•9 


4.9 
5.6 
6.3 


664 


217 


223 


230 


236 


243 


249 


256 


262 


269 


275 


!665 


282 


28s 


295 


302 


308 


315 


321 


328 


334 


341 






666 


347 


354 


366 


367 


373 


380 


386 


393 


399 


406 






667 


412 


419 


425 


432 


438 


445 


451 


458 


464 


471 






66S 


477 


484 


490 


497 


503 


510 


516 


523 


529 


536 






669 
670 

671 


542 


549 


555 


562 


568 


575 


58? 


588 


594 


601 




§ 


607 


614 


620 


627 


633 


640 


646 


653 


659 


666 


672 


67s 


685 


691 


698 


704 


711 


717 


724 


730 


672 


737 


743 


750 


756 


763 


769 


775 


782 


788 


795 


.1 


0-6 


673 


801 


808 


814 


821 


827 


834 


840 


846 


853 


859 


.2 
.■J 


1-3 

1.9 


674 


S66 


872 


879 


885 


892 


898 


904 


911 


917 


924 




675 


930 


937 


943 


949 


956 


962 


969 


975 


982 


988 


•4 


2.6 


676 


994 


"^OOI 


*oo7 


*oi4 


*026 


*027 


*o33 


*o39 


*o46 


*052 


•5 
.6 


3-2 

3-9 


677 


83 059 


065 


071 


078 


084 


091 


097 


103 


no 


116 




67S 


123 


129 


136 


142 


148 


155 


161 


168 


174 


180 


.7 


4-5 


679 
680 

681 


187 


193 


200 


206 


212 


219 


225 


231 


238 


244 


.8 
•9 


5-2 
5-8 


251 


257 


263 


270 


276 


^^3 


289 


295 


302 


308 


314 


321 


327 


334 


340 


346 


353 


359 


365 


372 


682 


378 


385 


391 


397 


404 


410 


416 


423 


429 


435 






683 


442 


448 


455 


461 


467 


474 


480 


486 


493 


499 






684 


505 


512 


518 


524 


531 


537 


543 


550 


556 


562 






685 


569 


575 


58? 


588 


594 


6o5 


607 


613 


619 


626 






686 


632 


638 


645 


65^ 


657 


664 


670 


676 


683 


689 




6 


687 


695 


702 


708 


714 


721 


727 


733 


740 


746 


752 


.1 


0.6 


688 


759 


765 


771 


778 


784 


790 


796 


803 


809 


815 


.2 

•3 

•4 
■5 
.6 


1.2 

T '^ 


689 
690 

691 


822 
885 


828 
891 


834 


841 


847 


853 


859 


866 


872 


878 


2.4 

3.0 
3.6 


897 


904 


910 


916 


922 


929 


935 


941 


948 


954 


960 


966 


973 


979 


985 


992 


998 


*oo4 


692 


84 010 


017 


023 


029 


035 


042 


048 


054 


061 


067 






693 


073 


079 


086 


092 


098 


104 


II I 


117 


123 


129 


•7 


4.2 


694 


136 


142 


148 


154 


161 


167 


173 


179 


186 


192 


.8 
•9 


4.3 
5.4 


695 


198 


204 


211 


217 


223 


229 


236 


242 


248 


254 


696 


261 


267 


273 


279 


286 


292 


298 


304 


311 


317 






.697 


Z2l 


329 


335 


342 


348 


354 


360 


367 


373 


379 






698 


385 


392 


398 


404 


410 


416 


423 


429 


435 


441 






699 
700 


447 


454 


460 


465 


472 


479 


485 


491 


497 503 






510 


516 


522 


528 


534 


541 


547 


553 


559 565 





1 


2 


3 


4 


5 


6 


7 


8 9 


P. 


P. 



13 



TABLE I. 



1 N. 
700 

701 





1 


2 


3 


4 


5 


6 


7 " 


8 


1) 


P 


P. 


84 510 
572 


516 


522 


528 


534 


541 


547 


553 


559 


565 






578 


584 


590 


596 


603 


609 


615 


621 


627 


702 


<^33 


640 


646 


652 


658 


664 


671 


677 


683 


689 






703 


695 


701 


708 


714 


720 


726 


732 


739 


745 


751 






704 


757 


763 


769 


776 


782 


788 


794 


8o5 


806 


813 






705 


819 


825 


831 


837 


843 


849 


856 


862 


868 


874 




6 


706 


885 


886 


893 


899 


905 


911 


917 


923 


929 


936 




707 


942 


948 


954 


960 


966 


972 


979 


985 


991 


997 


.2 


0.5 

1-3 


708 


85 003 


009 


015 


021 


028 


034 


040 


046 


052 


05 8 


•3 


1.9 


709 
710 

711 


064 


070 


077 


083 


089 


095 


lOI 


107 


113 


119 


• 4 
•5 
.6 


2.6 
3-2 

3-9 


126 


132 


138 


144 


150 


156 


162 


168 


174 


181 


187 


193 


199 


205 


21 ! 


217 


223 


229 


236 


242 


712 


248 


254 


260 


265 


272 


278 


284 


290 


297 


303 




^ 


713 


309 


315 


321 


327 


333 


339 


345 


351 


357 


363 


• 7 
.8 


4-5 

5-2 


7M 


370 


376 


382 


388 


394 


400 


406 


412 


418 


424 


•9 


5-8 


715 


430 


436 


443 


449 


455 


461 


467 


473 


479 


485 






716 


491 


497 


503 


509 


515 


521 


527 


533 


540 


546 






717 


552 


558 


564 


570 


576 


582 


588 


594 


600 


606 






1718 


612 


618 


624 


630 


636 


642 


648 


655 


661 


667 






1719 
720 

721 


673 


679 


685 


691 


697 


703 


709 


715 


721 


727 




6 

fi 


733 


739 


745 


751 


757 


763 


769 


775 


781 


787- 


793 


799 


805 


811 


817 


823 


829 


835 


841 


847 


722 


853 


859 


865 


872 


878 


884 


890 


896 


902 


908 


.2 


1 .2 


723 


914 


920 


926 


932 


93^ 


944 


950 


956 


962 


968 


■3 


1.8 


724 


974 


980 


986 


992 


998 


*oo4 


*OTO 


*oi6 


*022 


*028 






725 


86034 


040 


046 


052 


058 


063 


069 


075 


081 


087 


•4 
.5 


2.4 
3.0 


726 


093 


099 


105 


III 


117 


123 


129 


135 


141 


147 


.6 


3-6 


727 


153 


159 


165 


171 


177 


183 


189 


195 


201 


207 






728 


213 


219 


225 


231 


237 


243 


249 


255 


261 


267 


•7 
.8 


4.2 
4.8 


729 
730 

731 


273 


278 


284 


290 


296 


302 


3O8 


314 


320 


326 


'9 


5.4 


332 


338 


344 


350 


356 


362 


368 


374 


380 


386 


391 


397 


403 


409 


415 


421 


427 


433 


439 


445 


732 


451 


457 


463 


469 


475 


■481 


486 


492 


498 


504 






733 


510 


516 


522 


528 


534 


540 


546 


552 


558 


563 






734 


569 


575 


58i 


587 


593 


599 


605 


611 


617 


623 






73S 


628 


634 


640 


646 


652 


658 


664 


670 


676 


682 




s 


736 


688 


693 


699 


705 


711 


717 


723 


729 


735 


741 




737 


746 


752 


758 


764 


770 


776 


782 


788 


794 


800 


. I 

.2 


0-5 
I.I 


738 


805 


811 


817 


823 


829 


835 


841 


847 


852 


858 


.3 


1-6 


739 
740 

741 


864 


870 


876 


882 


888 


894 


899 


905 


911 


917 


•4 
•5 
.6 


2.2 

2.7 
3-3 


923 


929 


935 


941 


946 


952 


958 


964 


970 


976 


982 


987 


993 


999 


*oo5 


*OI I 


*oi7 


*023 


*028 


*034 


742 


87 040 


046 


052 


058 


064 


069 


075 


081 


087 


093 




« 


743 


099 


104 


no 


116 


122 


128 


134 


140 


145 


151 


■ 7 

.8 


3-8 
4.4 


744 


157 


163 


169 


175 


180 


186 


192 


198 


204 


210 


•9 


4.9 


745 


215 


221 


227 


233 


239 


245 


250 


256 


262 


268 






746 


274 


279 


285 


291 


297 


303 


309 


314 


320 


326 






747 


332 


338 


343 


349 


355 


361 


367 


372 


378 


384 






748 


390 


396 


402 


407 


413 


419 


425 


431 


436 


442 






749 
750 


448 


454 


460 


465 


471 


477 


483 


489 


494 


500 






506 


512 


517 


523 


529 


535 


541 


546 


552 


558 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


P. 


P. 



14 



LOGARITHMS OF NUMBERS. 



N." 


1 1 


1 i£ 


3 


4 


5 


G 


7 


8 


1> 


P. P. 


750 

751 


87 506 1 512 


517 


523 


529 


535 


541 


546 


552 


558 




564 


570 


575 


58? 


587 


593 


598 


604 


610 


616 


752 


622 


627 


633 


639 


645 


650 


656 


662 


668 


673 




753 


679 


685 


691 


697 


702 


708 


714 


720 


725 


731 




754 


737 


743 


748 


754 


760 


766 


771 


777 


783 


789 




755 


794 


800 


806 


812 


817 


823 


829 


835 


846 


846 




75^ 


852 


858 


863 


869 


875 


881 


886 


892 


898 


904 




6 


757 


909 


915 


921 


927 


932 


938 


944 


949 


955 


961 


.1 


0.6 


|75'^ 


967 


972 


978 


984 


990 


995 


*OOI 


*oo7 


*OI2 


*oi8 


.3 


1.8 


|Vb9 
760 
761 


88 024 


030 


035 


041 


047 


053 


058 


064 


070 


_^75 
^33 


•4 
•5 
.6 


2.4 
3-0 
3-6 


081 


087 


093 


098 


104 


no 


115 


121 


127 


138 


144 


150 


15s 


161 


167 


172 


178 


184 


190 


762 


195 


201 


207 


212 


218 


224 


229 


235 


241 


247 






7^3 


252 


258 


264 


269 


275 


28t 


286 


292 


298 


3°3 


■ 7 

Q 


4.2 

A R 


7b4 


309 


315 


320 


326 


332 


337 


343 


349 


355 


360 


•9 


5-4 


y^b 


366 


372 


377 


383 


389 


394 


400 


406 


411 


417 




766 


423 


428 


434 


440 


445 


451 


457 


462 


468 


474 




7b7 


479 


485 


491 


496 


502 


508 


513 


519 


525 


536 




708 


536 


542 


547 


553 


558 


564 


570 


575 


58i 


587 




709 
770 

771 


592 


598 


604 


609 


615 


621 


625 


632 


638 


643 




649 


654 


660 


666 


671 


677 


683 


688 


694 


700 


705 


711 


716 


722 


728 


733 


739 


745 


750 


756 




5 


I77-' 


761 


767 


773 


778 


784 


790 


795 


801 


806 


812 


.1 


0.5 


773 


818 


823 


829 


835 


840 


846 


851 


857 


863 


868 


.3 


1. 6 


1774 


874 


879 


885 


891 


896 


902 


907 


913 


919 


924 






775 


930 


936 


941 


947 


952 


958 


964 


969 


975 


980 


•4 


2.2 


77b 


986 


992 


997 


*oo3 


*oo8 


*oi4 


*oi9 


*025 


*o3i 


*o36 


■ 5 
.6 


2.7 
3.3 


1777 


89 042 


047 


053 


059 


064 


070 


075 


081 


087 


092 






I77S 


098 


103 


109 


114 


120 


126 


131 


^37 


142 


148 


• 7 


3-8 


779 
780 

I781 


153 


159 


165 


170 


176 


181 


187 


193 


198 


204 


.8 
.Q 


4.4 
A .n 


209 215 


220 


226 


231 


237 


243 


248 


254 


259 




265 


276 


276 


282 


287 


293 


298 


304 


309 


315 


j7&2 


320 


326 


332 


337 


343 


348 


354 


359 


365 


370 




17^3 


376 


381 


387 


393 


398 


404 


409 


415 


420 


426 




784 


431 


437 


442 


448 


454 


459 


465 


476 


476 


4S1 




I7«5 


487 


492 


498 


503 


509 


514 


520 


525 


531 


536 




786 


542 


548 


553 


559 


564 


570 


575 


581 


586 


592 




s 


7«7 


597 


603 


608 


614 


619 


625 


630 


636 


641 


647 


.1 


0.5 


788 


652 


658 


663 


669 


674 


680 


685 


691 


696 


702 


.2 


1 .0 


7&9 
790 

791 


707 


713 


718 


724 


729 


735 


740 


746 


751 


757 


•4 
•5 
.6 


2.0 

2-5 

3.0 


762 


768 


773 


779 


784 


790 


795 


801 


806 


812 


817 


823 


828 


834 


839 


845 


850 


856 


861 


867 


792 


872 


878 


883 


889 


894 


900 


905 


911 


916 


922 






793 


927 


933 


938 


943 


949 


954 


960 


965 


971 


976 


•7 
.8 

•9 


3-5 


794 


982 


987 


993 


998 


*oo4 


*oo9 


*oi5 


*025 


*026 


*o3i 


4.0 
4."; 


795 


90036 


042 


047 


053 


058 


064 


069 


075 


080 


086 




796 


091 


097 


102 


107 


113 


118 


124 


129 


135 


140 




797 


146 


151 


156 


162 


167 


173 


178 


184 


189 


195 




798 


200 


205 


211 


216 


222 


227 


233 


238 


244 


249 




799 
800 


254 


260 


265 


271 


276 


282 


287 


292 


298 


303 


1 


309 


314 


320 


325 


330 


336 


341 


347 


352 


358 


IN. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


P.P. 



15 













TABLE 


I. 












N. 





1 2 1 


3 


4 


5 


^ \ 


7 


8 


9 


P. P. 1 


800 

8oi 


90 309 


314 


320 


325 


330 


336 


341 


347 


352 


358 




363 


368 


374 


379 


385 


390 


396 


401 


406 


412 


802 


41? 


423 


428 


433 


439 


444 


450 


455 


466 


466 




803 


471 


477 


482 


488 


493 


498 


504 


509 


515 


520 




804 


525 


531 


536 


542 


547 


552 


558 


563 


569 


574 




80s 


579 


585 


590 


596 


601 


6og 


612 


617 


622 


628 




806 


633 


639 


644 


649 


655 


666 


666 


671 


676 


682 




807 


687 


692 


698 


703 


709 


714 


719 


725 


730 


736 




808 


741 


746 


752 


757 


762 


768 


773 


778 


784 


789 




809 
810 
811 


795 


800 


805 


811 


816 


821 


827 


832 


838 


843 


B 


848 


854 


859 


864 


870 


875 


886 


886 


891 


896 


902 


907 


913 


918 


923 


929 


934 


939 


945 


950 




0.5 
I.I 


812 


955 


961 


966 


971 


977 


982 


987 


993 


998 


*oo3 


.2 


«i3 


91 009 


014 


019 


025 


030 


036 


041 


046 


052 


057 


•3 


1-6 


814 


062 


068 


073 


078 


084 


089 


094 


100 


105 


1 16 






815 


116 


121 


125 


131 


137 


142 


147 


153 


158 


163 


•4 

.5 


2.7 


816 


169 


174 


179 


185 


190 


195 


201 


206 


211 


217 


.6 


3-3 


817 


222 


227 


233 


238 


243 


249 


254 


259 


264 


270 




3-8 
4.4 


818 


275 


280 


286 


291 


296 


302 


307 


312 


318 


323 


•7 

.8 


819 
820 

821 


328 


333 


339 


344 


349 

402 


355 


360 


3(^5 


371 


376 


•9 


4.9 


38i 


386 


392 


397 


408 


413 


418 


423 


429 




434 


439 


445 


450 


455 


461 


466 


471 


476 


482 


822 


487 


492 


497 


503 


508 


513 


519 


524 


529 


534 




823 


540 


545 


550 


556 


561 


5^6 


571 


577 


582 


587 




824 


592 


598 


603 


608 


614 


619 


624 


629 


635 


640 




825 


645 


656 


656 


661 


666 


671 


677 


682 


687 


692 




826 


698 


703 


708 


714 


719 


724 


729 


735 


740 


745 




827 


750 


756 


761 


766 


771 


777 


782 


787 


792 


798 




828 


803 


808 


813 


819 


824 


829 


834 


839 


845 


850 




829 
830 

831 


855' 


866 


866 


871 


876 


881 


887 


892 


897 


902 


r 


908 


913 


918 


923 


928 


934 


939 


944 


949 


955 


960 


965 


976 


976 


981 


986 


991 


996 


*002 


*oo7 


. I 



0.5 


832 


92 012 


017 


023 


028 


033 


038 


043 


049 


054 


059 


.2 


I.O 


833 


064 


069 


075 


080 


085 


090 


096 


lOI 


106 


III 


•3 


1-5 


834 


116 


122 


127 


132 


137 


142 


148 


153 


158 


163 


■4 

.5 


2 .0 


835 


168 


174 


179 


184 


189 


194 


200 


205 


210 


215 


2.5 


836 


220 


226 


231 


236 


241 


246 


252 


257 


262 


267 


.6 


3-0 


837 


272 


277 


283 


288 


293 


298 


303 


309 


314 


319 


• 7 
.8 


3-5 
4.0 


838 


324 


329 


335 


340 


345 


350 


355 


360 


366 


371 


839 
840 

841 


376 


381 


386 


391 


397 


402 


407 


412 


417 


423 


•9 


4-5 


428 


433 


438 


443 


448 


454 


459 


464 


469 


474 




479 


485 


490 


495 


500 


505 


510 


515 


521 


526 


842 


531 


536 


541 


546 


552 


557 


562 


5^7 


572 


577 




843 


583 


588 


593 


598 


603 


608 


613 


619 


624 


629 




844 


634 


639 


644 


649 


655 


660 


665 


670 


675 


686 




845 


685 


691 


696 


701 


706 


711 


716 


721 


727 


732 




846 


737 


742 


747 


752 


757 


762 


768 


773 


778 


783 




847 


788 


793 


798 


803 


809 


814 


819 


824 


829 


834 




848 


839 


844 


850 


855 


860 


865 


876 


875 


885 


885 




849 
850 


891 


896 


901 


906 


911 


916 


921 


926 


931 


937 




942 


947 


952 


957 


962 


967 


972 


977 


982 


988 


N. 





1 


3 


3 1 4 


5 


6 


7 


8 


9 


P. P. 



16 











LOGARITHMS OF NUMBERS. 








N. 





1 i 


*2 


~l5~ 


4 


5 1 6 1 


7 8 


1 


P. P. 


850 

851 


92 942 


947 


952 


957 


962 


967 


972 


977 982 


988 




993 


998 


*oo3 


*oo8 


*oi3 


*oi8 


*023 


*028 


"034 


*,o39 


«5-- 


93 044 


049 


054 


059 


064 


069 


074 


079 


084 


090 




853 


095 


100 


105 


1 10 


n5 


120 


125 


130 


135 


140 




854 


146 


151 


156 


161 


166 


171 


176 


181 


186 


191 




855 


196 


201 


207 


212 


217 


222 


227 


232 


237 


242 




856 


247 


252 


257 


262 


267 


272 


278 


283 


288 


293 




5 


857 


298 


303 


308 


313 


318 


323 


328 


333 


338 


343 


.1 


0.5 


858 


348 


354 


359 


364 


369 


374 


379 


384 


389 


394 


• 3 


1.6 


859 
860 

861 


399 


404 


409 


414 


419 


424 


429 


434 


439 


445 


•4 

•5 
.6 


2.7 
3-3 


450 


455 


460 


465 


470 


475 


480 


485 


490 


495 


506 


505 


510 


5^5 


520 


525 


530 


53§ 


546 


545 


862 


550 


556 


561 


566 


571 


576 


581 


586 


591 


596 






863 


601 


606 


611 


616 


621 


626 


63? 


636 


641 


646 


• 7 
8 


3-S 


864 


655 


656 


661 


666 


671 


676 


681 


686 


691 


696 


•9 


4.4 
4.9 


865 


701 


706 


711 


716 


721 


726 


731 


736 


742 


747 




866 


752 


757 


762 


767 


772 


777 


782 


787 


792 


797 




867 


802 


807 


812 


817 


822 


827 


832 


837 


842 


847 




868 


852 


857 


862 


867 


872 


877 


882 


887 


892 


897 




869 
870 

871 


902 


907 


912 


917 


922 


927 


932 


937 


942 


947 




952 957 


962 1 967 


972 


977 


982 


987 


992 


997 


94 002 


007 


012 


017 


022 


026 


031 


<^36 


041 


046 




5 


872 


051 


056 


061 


065 


071 


076 


081 


086 


091 


096 


.1 


0.5 
I 


873 


lOI 


106 


ITI 


116 


121 


126 


131 


136 


141 


146 


• 3 


1-5 


874 


151 


156 


161 


166 


171 


176 


181 


186 


191 


196 






875 


201 


206 


210 


215 


220 


225 


230 


235 


240 


245 


■4 


2.0 


J876 


250 


255 


260 


265 


270 


275 


280 


285 


290 


295 


•5 
.6 


2-5 

3-0 


877 


300 


305 


310 


315 


320 


324 


329 


334 


339 


344 






878 


349 


354 


359 


364 


369 


374 


379 


384 


389 


394 


• 7 
.8 

•9 


3-5 


879 
880 
881 


399 


404 


409 


413 


418 


423 


428 


433 


438 


443 


4.0 


448 ' 453 


458 


463 


468 


473 


478 


483 


487 


492 




497 


502 


507 


512 


517 


522 


527 


532 


537 


542 


882 


547 


552 


556 


561 


566 


571 


576 


58i 


586 


591 




883 


596 


601 


606 


611 


615 


620 


625 


630 


635 


640 




884 


645 


650 


655 


660 


665 


670 


674 


679 


684 


689 




885 


694 


699 


704 


709 


714 


719 


724 


728 


733 


738 




886 


743 


748 


753 


758 


763 


768 


773 


777 


782 


787 




4 


887 


792 


797 


802 


807 


812 


817 


821 


826 


83? 


836 


.1 


0.4 


888 


841 


846 


851 


856 


861 


865 


870 


875 


880 


885 


.3 


U.9 
1-3 


889 
890 
891 


890 


895 


900 


905 


909 


914 


919 


924 


929 


934 


.4 

■ 5 
.6 


1.8 
2.2 
2.7 


939 


944 


949 1 953 


958 


963 


968 


973 


978 


983 


988 


992 


997 j*002 


*oo7 


*OI2 


*oi7 


*022 


*026 


031 


892 


95 036 


041 


046 


051 


056 


061 


065 


070 


075 


o85 






893 


085 


090 


095 


099 


104 


109 


114 


119 


124 


129 


■7 
8 


3-1 
3.6 
4.0 


894 


134 


138 


143 


148 


153 


158 


163 


167 


172 


177 


•9 


895 


182 


187 


192 


197 


201 


206 


211 


216 


221 


226 




896 


231 


235 


240 


245 


250 


255 


260 


264 


269 


274 




897 


279 


284 


289 


294 


298 


303 308 


3^3 


318 


323 




898 


327 


332 


337 


342 


347 


352 i 356 


361 


3^6 


371 




899 
900 

N. 


376 


381 


385 


390 


395 


400 405 


410 


414 


419 




424 


429 


1 434 1 438 


443 


448 453 


458 


463 


467 





1 


2 j 3 


4 


5 t 6 


7 1 8 


9 


P. P. 



17 







• 






TABLE 


I. 














N. 





1 


2 


3 


4 


5 


~ii~ 


7 


8 


9 


P. P. i 




900 

901 


95 424 
472 


429 


434 


438 


443 


448 


453 


458 


463 


467 


1 




477 


482 


487 


492 


496 


501 


506 


511 


516 




902 


520 


525 


530 


535 


540 


544 


549 


554 


559 


564 






9°3 


569 


573 


578 


583 


588 


593 


597 


602 


607 


612 






904 


617 


621 


625 


631 


636 


641 


645 


650 


655 


660 






905 


665 


669 


674 


679 


684 


689 


693 


698 


703 


708 






906 


713 


717 


722 


727 


732 


737 


741 


746 


751 


756 






907 


766 


765 


770 


775 


780 


784 


789 


794 


799 


804 






908 


808 


813 


818 


823 


827 


832 


837" 


842 


847 


855 






909 
910 
911 


856 


861 


866 


870 


875 


880 


885 


890 


894 


899 






904 


909 


913 


918 


923 


928 


933 


937 


942 


947 




952 


956 


961 


966 


971 


975 


986 


985 


990 


994 




5 




912 


999 


*oo4 


*oo9 


*oi4 


*oi8 


*62s 


*028 


*o33 


*o37 


*042 


.1 


0.5 




913 


96 047 


052 


05 6 


061 


066 


071 


075 


086 


085 


090 


.3 


1-5 




914 


094 


099 


104 


109 


113 


118 


123 


128 


132 


137 








915 


142 


147 


151 


156 


161 


166 


170 


17s 


180 


185 


•4 


2.0 




916 


189 


194 


199 


204 


208 


213 


218 


222 


227 


232 


•5 
.6 


2-5 

3-0 




917 


237 


241 


246 


251 


256 


266 


265 


270 


275 


279 








918 


284 


289 


293 


298 


303 


308 


312 


317 


322 


327 


•7 
.8 
.Q 


3-5 




919 
920 

921 


331 


336 


341 


345 


350 


355 


360 


364 


369 


374 


4.0 
A.e. 




379 


383 


388 


393 


397' 


402 


407 


412 


416 


421 






426 


430 


435 


440 


445 


449 


454 


459 


463 


468 




922 


473 


478 


482 


487 


492 


496 


501 


506 


511 


515 






923 


520 


525 


529 


534 


539 


543 


548 


553 


558 


562 






924 


567 


572 


576 


58i 


586 


590 


595 


600 


605 


609 






925 


614 


619 


623 


623 


633 


637 


642 


647 


65? 


656 






926 


661 


666 


670 


675 


680 


684 


689 


694 


698 


703 






I927 


708 


712 


717 


722 


726 


731 


736 


741 


745 


750 






I928 


755 


759 


764 


769 


773 


778 


783 


787 


792 


797 






,929 
930 

931 


801 


806 


8ri 


815" 


820 


825 


829 


834 


839 


843 






848 


853 


857" 


862 


867 


871 


876 


881 


885 


890 




895 


899 


904 


909 


913 


918 


923 


927 


932 


937 




4 




932 


941 


946 


951 


955 


960 


965 


969 


974 


979 


983 




0.4 




933 


988 


993 


997 


*002 


*oo7 


*OII 


*oi6 


*020 


*025 


*o3° 


•3 


1-3 




934 


97 034 


039 


044 


048 


053 


058 


062 


067 


072 


076 








935 


081 


086 


090 


095 


099 


104 


109 


113 


118 


123 


•4 


1.8 




936 


127 


132 


137 


141 


146 


151 


^55 


160 


164 


169 


•5 
.6 


2.7 




937 


174 


178 


183 


188 


192 


197 


202 


205 


211 


215 








93« 


220 


225 


229 


234 


239 


243 


248 


252 


257 


262 


•7 

.8 

•9 


3-1 
3-6 

d.O 




939 
940 

941 


265 


271 


276 


280 


285 


289 


294 


299 


303 


308 




3^3 


317 


322 


326 


331 


336 


340 


345 


349 


354 






359 


363 


368 


373 


377 


382 


386 


391 


396 


400 




942 


405 


409 


414 


419 


423 


428 


432 


437 


442 


446 






943 


451 


45^ 


460 


465 


469 


474 


479 


483 


488 


492 






944 


497 


502 


506 


511 


515 


520 


525 


529 


534 


538 






945 


543 


548 


552 


557 


56i 


566 


570 


575 


580 


584 






946 


589 


593 


598 


603 


607 


612 


616 


621 


626 


636 






947 


635 


639 


644 


649 


653 


658 


662 


667 


671 


676 






948 


681 


685 


690 


694 


699 


703 


708 


713 


717 


722 






949 
950 


726 


731 


73f> 


740 


745 


749 


754 


758 


763 


768 






772 


777 


781 


786 


796 


795 


800 


804 


809 


813 




N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


P.P. 





iS 









LOGARITHMS OF 


NUMBERS. 










1 N. 





1 


2 


3 


4 


5 





'7 


8 


9 


P. P. 


950 

' 951 


97 772 


777 


781 


786 


796 


795 


800 


804 


809 


813 




818 


822 


827 


83? 


836 


841 


845 


850 


854 


859 


952 


863 


868 


873 


877 


882 


886 


891 


895 


900 


904 




953 


909 


914 


918 


923 


927 


932 


936 


941 


945 


95° 




' 954 


955 


959 


964 


968 


973 


977 


982 


986 


991 


996 




955 


98 006 


005 


009 


014 


oig 


023 


027 


032 


03 6 


041 


S 


956 


046 


050 


055 


059 


064 


068 


073 


07? 


082 


086 


.1 


0.5 


957 


091 


095 


100 


105 


109 


114 


"8 


123 


127 


132 


.2 


1.0 


95S 


136 


141 


145 


150 


154 


159 


163 


168 


173 


177 


• 3 


1-5 


959 
9<J0 

961 


182 
227 
272 


186 


191 


195 


200 


204 


209 


213 


218 


222 


•4 

•5 
.6 


2.0 

2-5 

3-0 


231 


236 


240 


245 


^'^1^ 


^54' 


259 


263 


268 


277 


281 


286 


296 


295 


299 


304 


308 


3^3 


96. 


3-7 


322 


326 


35^ 


335 


340 


344 


349 


353 


358 


•7 


3-5 


963 


362 


367 


371 


376 


3S6 


385 


389 


394 


398 


403 


.8 


4.0 


964 


4of 


412 


416 


421 


425 


430 


434 


439 


443 


448 


•9 


4-5 


965 


452 


457 


461 


466 


476 


475 


479 


484 


488 


493 




966 


497 


502 


506 


511 


515 


520 


524 


529 


533 


538 




967 


542 


547 


551 


556 


560 


565 


569 


574 


578 


583 




96S 


587 


592 


596 


601 


605 


610 


614 


619 


623 


628 




1 969 
1 970 

971 


632 


637 


641 


646 


650 


655 


659 


663 


668 


672 


. 4 


677 


681 


686 


690 


695 


699 


704 


708 


713 


717 


722 


726 


731 


735 


740 


744 


749 


753 


757 


762 


.1 


0.4 


972 


766 


771 


775 


780 


784 


789 


793 


798 


802 


807 


.2 


0.9 


973 


811 


815 


820 


824 


829 


833 


838 


842 


847 


85 i 


•3 


1.3 


974 


856 


860 


865 


869 


873 


878 


882 


887 


891 


896 


•4 


1.8 


975 


906 


905 


909 


914 


9^8 


922 


927 


931 


936 


946 


•5 


2.2 


j 976 


945 


949 


954 


958 


963 


967 


971 


976 


980 


985 


.6 


2.7 


977 


989 


994 


998 


*oo3 


*oo7 


*OII 


*oi6 


*020 


*025 


*029 


• 7 


3-i 


978 


99 034 


038 


043 


047 


051 


056 


060 


065 


069 


074 


.8 


3-6 


979 
980 

981 


078 


082 


087 


091 


096 


ICO 


105 


109 


113 


118 


•9 


4.0 


122 


127 


131 


136 


140 


145 


149 


153 


158 


162 




167 


171 


176 


180 


184 


189 


193 


198 


202 


205 


982 


211 


215 


220 


224 


229 


233 


237 


242 


246 


251 




983 


255 


260 


264 


26§ 


273 


277 


282 


286 


290 


295 




984 


299 


304 


308 


312 


317 


321 


326 


330 


335 


339 




985 


343 


348 


352 


357 


361 


365 


370 


374 


379 


383 


4 


986 


387 


392 


396 


401 


405 


409 


414 


418 


423 


427 


.1 


0.4 


987 


431 


436 


440 


445 


449 


453 


458 


462 


467 


471 


.2 


0.8 


988 


475 


480 


484 


489 


493 


497 


502 


506 


511 


515 


•3 


1.2 1 


i 989 
990 
991 


519 


524 


528 


533 


537 


541 


546 


556 


554 


559 


•4 
•5 
.6 


1.6 
2.0 
2.4 


563 
607 


568 


572 


576 


581 


585 


590 


594 


598 


603 


611 


616 


620 


625 


629 


^33 


638 


642 


647 


992 


651 


655 


660 


664 


668 


673 


677 


682 


686 


696 


•7 


2.8 


993 


695 


699 


703 


708 


712 


717 


721 


725 


730 


734 


.8 


3-2 


994 


738 


743 


747 


751 


756 


766 


765 


769 


773 


778 


•9 


3-6 


995 


782 


786 


791 


795 


800 


804 


808 


813 


817 


821 




996 


826 


836 


834 


839 


843 


847 


852 


856 


861 


865 




997 


869 


874 


878 


882 


887 


891 


895 


900 


904 


908 




! 998 


913 


917 


922 


926 


930 


935 


939 


943 


948 


952 




999 
1000 


956 

00 000 


961 


965 


969 


974 


978 


982 


987 


991 


995 




004 


cog 


013 


017 


021 


026 


030 


034 


039 


N. 


1 


1 2 1 


3 1 4 


5 


6 


7 


8 


9 


P.P. 



19 



TABLE I. 



IFn." 





1 


2 1 3 


4 


5 1 6 


7 


8 


9 


P. P. It 


1 1000 

OI 


000 000 
434 


043 


087 


130 


173 


217 


266 


304 


347 


390 






477 


521 


564 


607 


651 


694 


737 


781 


824 


02 


867 


911 


954 


997 


*04i 


*o84 


*I27 


*i7i 


*2I4 


*257 






03 


001 301 


344 


387 


431 


474 


517 


566 


604 


647 


696 






04 


733 


777 


820 


863 


906 


950 


993 


*o36 


*o79 


*I23 






05 


002 166 


209 


252 


295 


339 


382 


425 


468 


511 


555 






06 


598 


641 


684 


727 


770 


814 


857 


900 


943 


986 






07 


003 029 


072 


115 


159 


202 


245 


288 


33^ 


374 


417 


A? 


43 


08 


466 


503 


546 


590 


(>33 


676 


719 


762 


805 


848 


.1 


i-^ 


4-3 


09 

1010 

II 


891 


934 


977 


*020 


*o63 


*io6 


*i49 


*192 


*235 


*278 


.2 

•3 

•4 
•5 
.6 


13.0 
17.4 

21.7 

26. 1 


8.6 
12.9 

17.2 

21-5 

25.8 


004 321 
75^ 


364 


407 


450 


493 


536 


579 


622 


665 


708 


794 


837 


880 


923 


966 


*oo9 


*o5i 


*094 


*i37 


12 


005 180 


223 


266 


309 


352 


395 


438 


481 


523 


566 








13 


609 


652 


695 


738 


781 


824 


866 


909 


952 


995 


:8 


30.4 

34.8 


30.1 
34-4 


14 


006 038 


081 


123 


165 


209 


252 


295 


337 


386 


423 


•9 


391 


38.7 


15 


466 


509 


551 


594 


637 


680 


722 


765 


808 


851 






16 


893 


936 


979 


*02 2 


*o64 


*io7 


*i5o 


*i93 


*235 


*278 






17 


007 321 


3^3 


406 


449 


491 


534 


577 


620 


662 


705 






18 


748 


790 


833 


875 


918 


961 


*oo3 


*046 


*o89 


131 






19 

1020 

21 


008 174 


217 


259 


302 


344 


387 


430 


472 


515 


557 






600 
009 025 


642 


685 


728 


770 


813 


855 


898 


946 


983 


063 


III 


153 


196 


238 


281 323 


366 


408 


22 


451 


493 


536 


S78 


621 


663 


706 1 748 


796 


833 


42 


42 


23 


875 


918 


960 


*oo3 


*045 


*o88 


*i3o 


*I72 


*2I5 


*257 


.2 


4i! 

8.5 


8.4 


24 


010 300 


342 


385 


427 


469 


512 


554 


596 


639 


681 


■3 


12.7 




i 25 


724 


766 


808 


851 


893 


935 


978 


*026 


*o62 


*io5 


•4 


17.0 


16.8 


i 26 


on 147 


189 


232 


274 


3^6 


359 


401 


443 


486 


528 


.6 


25-5 


25.2 


27 


570 


612 


655 


697 


739 


782 


824 


86fi 


908 


951 


•7 


2Q.7 


29.4 


28 


993 


*o35 


*o77 


*I20 


*l62 


*204 


*246 


*288 


*33^ 


*373 


.8 
■ 9 


34.0 
38.2 


33-6 
37.8 


1 29 
11030 

3^ 


012 415 


457 


500 


542 


584 


625 

*048 


668 


710 


753 


795 






837 


879 


921 


963 


*oo6 


*090 


*I32 


174 


216 


013 258 


301 


343 


385 


427 


469 


511 


553 


595 


637 


32 


679 


722 


764 


806 


848 


890 


932 


974 


*oi6 


*058 






1 33 


014 100 


145 


184 


226 


263 


310 


352 


394 


436 


478 






34 


520 


562 


604 


646 


688 


730 


772 


814 


856 


898 






35 


940 


982 


*024 


*o66 


*io8 


*i5o 


*I92 


*234 


*276 


*3iS 






36 


015 360 


401 


443 


485 


527 


569 


611 


653 


695 


737 


AI 


41 


1 37 


779 


820 


862 


904 


946 


988 


*o3o 


*072 


*ii3 


155 


.1 


4-1 


4.1 


1 3« 


016 197 


239 


281 


323 


364 


406 


448 


490 


532 


573 


•3 


12.4 


12.3 


i 39 
1640 

1 41 


61S 


657 


699 


741 


782 


824 


866 


908 


950 


991 


•4 
■5 
.6 


16.6 
20.7 
24.9 


16.4 
20.5 
24.6 


017 033 


075 


117 


158 


206 


242 


284 


325 


367 


409 


450 


492 


534 


576 


617 


659 


701 


742 


784 


826 


I 42 


867 


909 


951 


992 


*034 


*o76 


*ii7 


*i59 


*20I 


*242 


•7 
.8 


33-2 


2».7 

32.8 


43 


018 284 


326 


367 


409 


451 


492 


534 


575 


617 


659 


■9 


37-3 


36.9 


44 


706 


742 


783 


825 


867 


908 


950 


991 


*033 


*o74 






45 


019 1X6 


158 


199 


241 


282 


324 


365 


407 


448 


490 






46 


531 


573 


614 


656 


697 


739 


786 


822 


863 


905 






47 


946 


988 


*029 


*o7i 


*II2 


*i54 


*i95 


*237 


*278 


*320 






48 


020 361 


402 


444 


485 


527 


568 


610 


65 J 


692 


734 






49 
i 1050 


775 


817 


858 


899 


941 


982 1*024 


*o65 


*i06 


*i48 






021 189 


236 


272 


313 


354 


396 1 437 


478 


520 561 


U. 





1 


2 


3 4 


5 6 


7 8 9 P. P 


• 









LOGARITHMS OF 


NUMI 


3ERS. 










~N. 





1 


»> 


3 


4 


r> (i 7 


8 


J) 


1*. P. 


1050 

51 


021 1S9 


230 


272 


313 


354 


396 


437 i 478 


520 


5^1 


' 


602 


644 


685 


726 


768 


809 


856 


892 


933 


974 


52 


022 015 


057 


098 


139 


181 


222 


263 


304 


346 


387 


4I 


53 


428 


469 


511 


552 


593 


634 


676 


717 


758 


799 


.1 


41 

8 X 


54 


840 


882 


9^3 


964 


*ooS 


*046 


*o88 


*I29 


*i7o 


*2I I 


• 3 


° i 
12.4 j 


55 


023 252 


293 


335 


376 


417 


458 


499 


540 


58I 


623 


■ 4 


16.6 


56 


664 


705 


746 


787 


82g 


869 


916 


951 


993 


*034 


■ 5 

.6 


20.7 
24.9 


57 


024 075 


116 


157 


198 


239 


280 


321 


362 


403 


444 






58 


485 


526 


568 


609 


650 


691 


732 


773 


814 


855 


• 7 
.8 


33-2 


59 
lOGO 

61 


896 


937 


978 


*oi9 


*o6o 


*ior 


*I42 


*i83 


*224 


*265 


•9 


37.3 


025 306 


347 


38S 


429 


469 


510 


_55l 


592 


633 


674 




715 


756 


797 


838 


879 


920 


961 


*002 


*042 


*o83 


62 


026 124 


165 


205 


247 


288 


329 


370 


410 


451 


492 


41 


63 


533 


574 


615 


656 


696 


737 


778 


819 


860 


901 


.1 ' " 
.2 


4.1 

8.2 


64 


941 


982 


*023 


*o64 


*io5 


*i4S 


*i86 *227 


*26S 


*309 


•3 


12.3 


65 


027 349 


390 


431 


472 


512 


553 


594 635 


675 


716 


•4 

e 


16.4 


66 


757 


798 


838 


879 


920 


961 


*OOI 


*042 


*o83 


*I23 


.6 


20 . 5 
24.6 


67 


028 164 


205 


246 


285 


327 


368 


408 


449 


490 


530 


•7 


28.7 


68 


571 


612 


652 


693 


734 


774 


815 


856 


896 


937 


.8 
■9 


32 8 

?6.Q 


i 69 
1070 

71 


977 

029 384 

789 


*oi8 


*o59 


*099 


*i40 


*i8i 


*22i 


*262 


*302 


*343 
749 


aR 


424 


465 


505 


546 


586 


627 


668 


708 


830 


870 


911 


951 


992 


*032 


*o73 


*ii4 


*i54 


72 


030 195 


235 


276 


316 


357 


397 


438 


478 


519 


559 


.1 


t^ 1 

4.0 


73 


599 


640 


680 


721 


761 


802 


842 


883 


923 


964 


.2 
.3 


8.1 
12. 1 


74 


031 004 


044 


085 


I2§ 


166 


205 


247 


287 


327 


368 






75 


408 


449 


489 


529 


570 


610 


J^' 


691 


731 


772 


■4 
•5 


20.2 


76 


812 


852 


893 


933 


973 


*oi4 


*o54 


*094 


*i35 


*i75 


.6 


24-3 


77 


032 215 


256 


296 


336 


377 


417 


457 


498 


538 


578 


•7 

.8 


28.3 

32.4 


78 


619 


659 


699 


739 


7S0 


820 


866 


900 


941 


981 


•9 


36-4 


I 79 
1080 

81 


033 021 


061 


102 


142 


182 


222 


263 


303 


343 


383 


An 


424 
825 


464 


504 


544 


584 


625 


665 


705 


745 


785 


866 


906 


946 


986 


*026 


*o66 


*io7 


147 


187 


82 


034 227 


267 


307 


347 


388 


428 


468 


50S 


548 


588 


.1 


4.0 


83 


623 


66§ 


708 


748 


789 


829 


869 


909 


949 


989 


.2 
■ 3 


8.0 
12.0 


84 


035 029 


069 


109 


149 


189 


229 


269 


309 


349 


389 


■4 


16.0 


85 


429 


470 


510 


550 


590 


630 


670 


710 


750 


790 


•5 


20.0 


86 


830 


870 


910 


950 


990 


*029 


*o69 


*io9 


*i49 


*i89 


.6 


24.0 


87 


036 229 


269 


309 


349 


389 


429 


469 


509 


549 


589 


•7 
.8 


28.0 
32.0 


! 88 


629 


669 


708 


748 


788 


828 


868 


908 


948 


988 


•9 


36.0 


89 
1090 

91 


037 028 


068 


107 


147 


187 


227 


267 


307 


347 


386 


•?o 


426 


466 


506 


546 


586 


625 


665 


705 


745 


785 


825 


864 


904 


944 


984 


*023 


*o63 


*io3 


143 


183 


92 


038 222 


262 


302 


342 


38? 


421 


461 


501 


540 


580 


.1 


3-9 


93 


620 


660 


699 


739 


779 


819 


858 


898 


938 


977 


.2 
•3 


7-9 


94 


039 017 


057 


098 


136 


176 


216 


255 


295 


335 


374 


•4 


15.8 


95 


414 


454 


493 


533 


572 


612 


652 


691 


731 


771 


■5 
5 


19.7 


96 


810 


850 


890 


929 


969 


*oo8 


♦048 


*oS8 


*I27 


*i67 




:>■ 1 


97 


040 205 


246 


286 


325 


365 


404 


444 


483 


523 


563 


•7 
.8 


27-6 

31.6 


98 


602 


642 


681 


721 


760 


800 


839 


879 


9^8 


958 


•9 


35-5 


99 
1100 


997 
041 392 


*o37 


*o76 


*ii6 


*i55 


*i95 


*234 


*274 


*3^3 


*353 


1 


432 


471 


511 


550 


590 


629 


669 


708 


748 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


P. P. 



TABLE II.— CONSTANTS. 



Table for passing from 






Part I. 




Table for passing from 




[•log 


to/ 


LOGARITHMIC CONSTANTS. 


/ 


to log 




I 

2 

3 

4 
5 
6 

7 
8 

9 


2.30 258 509 
4.60 517 Olg 

6.90775528 

9.21034037 
II. 51 292546 

13.81 551 056 

16. II 809 565 
18.42068074 
20.72 326 583 


e — base of Naperian system 
I — Modulus of Naperian system 

Numbers. 
M = 0.43 429 448 19 

^=2.3025850930 

^ = 2.71 828 182 84 


10 = base of common system 
M = Modulus of common systerc 

log N = MIN. 

Common Logarithms. 
9.63 77S 431 -10 

0.36 221 570 

M 


1 '° 
20 

3 

4 
5 
6 

7 
8 

9 


4.34294482 
8.68588964 

1.30288344 
1-73717793 
2.17 147 241 
2.60576689 

3.04006 137 

3-47435585 
3.90865033 




Part II. 
CIRCULAR AND SPHERICAL CONSTANTS. 

jr — ratio of circumference to diameter of circle. C = circumference of circle. A = area of circle. 
.$■ = surface of sphere. F= volume of sphere. /? = radius. Z) = diameter. 




Table of Expressions for 




! ^ 


j:> 


C 


A 


-5- 


V 




J? 

1 


2R 


2nR 


TtR" 


47tR' 


%rcR' 




in 


D 


TtD 


IrtD' 


ttV 


\nD^ 




27t 


7t 


C 


47r 


7T 


67r=^ 




^ 7t 


^ 71 


2\/nA^ 


A 


4A 


3 TT 




2 ^ n 


. ' 7t 


sHtS^ 


IS 


s 


6 ^ 7t 




2 ^ 7t 


It 


|/6^^ V^ 


3 2 




» 


V 




i|/36;r V 


Vzbn V 




Numbers. 
AfTl = 12.56 637 061 
27t = 6.28318536 
^= 3-14159265 

f ;r = 4.18 879 020 
iTT = 0.78 539 816 
i;r= 0.52359877 

^= 0.31830988 

— = 0-15 915 494 

— = 0-07957747 
47r 

tt" = 9.86 960 440 
^„ = 0.01688685 

2i/^= 3.54490770 

Vtt = 1.77 245 385 


Logarithms. 
1.09 920 985 
0.79 817 987 
0.49714987 
0.62 208 86r 

9.89 508 988—10 
9.71 899 862 — 10 

9.50 285 012 — 10 
9.20 182 013— 10 

8.90 079 013—10 
0.99429974 
8.22 754 906-10 

0.54 960 493 
0.24857493 


Numbers. 
2V ^= I-I28379I6 

y ^ = 0.56 418 958 

^r ^ = 0.75 225 278 

: -y - = 0.09403 159 

V^^ = 4-83 597 586 
i /A 

y — = 1.24 070 098 

1 TT 

1 

|/;r = 1.46 459 189 

|/;r' = 2.14502 939 

|/6^' = 3.89 777 709 


Logarithms. 
0.05 245 506 

9.75 142505—10 

9.87 636 380—10 

8-97 327 381 — 10 
0.68 448 412 
0,09 366 712 

0.16 571 ()(i2 
0.33 143325 
0.59 081 700 





TABLE 11.— CONSTANTS. 



Part III. 

ANGULAR CONSTANTS. 

p = unit of circular measure, i.e., angle at centre of circle which intercepts 
an arc equal in length to the radius. 

360° = 27r. 180° = TT. 



Numbers. 1 


Logarithms. 


360"- 


360° 


2.55 630 250 


360° = 


2 1 600' 


4-33 445 375 


360° = 


I 296 000" 


6.1 1 260 500 


360° = 


24 hours 


1.38 021 124 


360° = 


I 440 minutes 


3.15 836249 


360° = 


86 400 seconds 


4.93651 374 


I hour = 


15° 


1. 17 609 126 


I hour = 


900' 


2.95424251 


I hour = 


54 000" 


4-73239376 


TV 


57°-29 577 95i 


1.75 812 263 


, 10800' 


57°i7'44".8o6 
3437'.74 677078 


3-53627388 


„ _ 648 000" _ 

7t 


206 264".8o 624 


5.31 442 513 


-(a = 


3^.81971 863 


0.58203 13^ 


/720\ 
\ ^ Ixa. 


229^.18311 805 


2.36 018 262 


-=mr 


13 7508-98 7083 


4-13833387 


ir = 90° = f = 


1-57079632 


0.19 611 987 


60° = ^ = 
3 


1.04 719 755 


0.02 002 862 


180 


o.oi 745 329 


8.24 187 737 — 10 


i'- "" - 


0.00 029 089 


6.46 372 611 — 10 


10 800 


1"- "" - 


0.00 000 485 


4.68557485-10 


64 8000 


TT _ 
** ~ 12 ~ 


0.26 179 939 


9.41 796 862 — 10 


71 
""" 720 ~~ 


0.00436332 


7.63981 737-10 


7C 


0.00 007 272 


5.86 166 612 — 10 



43 200 



23 



TABLE III. 



j log sin = log 0" + S. 




0° 


log 


" = log 


sin 0-f- S'. 


j log tan = log <p" -f- ^. 




log 


" = log 


tan 0+ 7". 


! " 


' 


S 


T 


Log. Sin. 


S' 


T 


Log. Tan. 


O 





4.685 5^ 


Sf 


— CO 


5-31442 


42 


— 00 


6o 


I 


57 


Sf 


6.46 372 


42 


42 


6.46 372 


I20 


2 


5? 


Sf 


•76475 


42 


42 


•76475 


i8o 


3 


Sf 


sf 


.94 084 


42 


42 


.94084 ^ 


j 240 


4 


57 


sf 


7.06 578 


42 


42 


7.06 578 


300 


5 


4.685 sf 


sf 


7.16 269 


5-31442 


42 


7.16 269 


360 


6 


5? 


s? 


.24 187 


42 


42 


.24188 


j 420 


7 


Sf 


57 


.30 882 


42 


42 


.30 882 


i 480 


8 


Sf 


57 


.36681 


42 


42 


.36681 


540 


9 


Sf 


57 


.41 797 


42 


42 


•41 797 


, 600 


10 


4.685 sf 


S? 


7.46372 


5-31442 


42 


7.46 372 


, 660 


II 


57 


Sf 


.50512 


42 


42 


.50512 


1 720 


12 


Sf 


Sf 


■ 54 290 


42 


42 


.54291 


i 780 


13 


Sf 


Sf 


•57 767 


42 


42 


• 57767 


840 


14 


Sf 


sf 


.60 98? 


42 


42 


.60985 


900 


15 


4.685 57 


58 


7.63 981 


5-31442 


42 


7.63 982 


1 960 


16 


Sf 


58 


.66 784 


42 


42 


.66 785 


! 1020 


17 


Sf 


58 


•6941? 


42 


42 


.69418 


1080 


18 


sf 


58 


.71 899 


42 


42 


.71 900 


I 140 


19 


sf 


58 


•74 248 


42 


42 


.74 248 


1200 


20 


4.685 57 


58 


7^76475 


5.31443 


42 


7-76 476 


1 1260 


21 


57 


58 


.78 594 


43 


42 


.78 595 


' 1320 


22 


57 


58 


.80614 


43 


42 


.8o6i§ 


1 1380 


23 


57 


58 


.82 545 


43 


42 


.82 546 


, 1440 


24 


57 


58 


•84 393 


43 


42 


.84 394 


1500 


25 


4.685 57 


58 


7.86 166 


5-31443 


41 


7.86 16^ 


1 1560 


26 


57 


58 


.87 869 


43 


41 


.87871 


1620 


27 


57 


58 


.89 508 


43 


41 


.89 510 


; 1680 


28 


57 


58 


.91 088 


43 


41 


.91 089 


1740 


29 


57 


58 


.92 612 


43 


41 


.92613 


j 1800 


30 


4.685 57 


58 


7.94 084 


5-31443 


41 


7.94 086 


1 i860 


31 


57 


58 


•95 508 


43 


41 


.95510 


1 1920 


32 


57 


58 


.96 887 


43 


41 


.96 889 


i 1980 


33 


57 


59 


.98 223 


43 


41 


.98 225 


! 2040 


34 


57 


59 


•99 520 


43 


41 


•99 522 


j 2100 


35 


4.685 56 


59 


8.00 778 


5-31443 


41 


8.00781 


i 2160 


36 


56 


59 


.02 002 


43 


41 


.02 004 


2220 


37 


5S 


59 


.03 192 


43 


41 


.03 194 


1 2280 


38 


56 


59 


•04 350 


43 


40 


.04 352 


i 2340 


39 


56 


59 


.05 478 


43 


40 


.05 481 


1 2400 


40 


4.685 56 


59 


8.06 S7f 


5-31443 


46 


8.06 586 


2460 


41 


56 


59 


.07 650 


43 


40 


.07 653 


2520 


42 


56 


59 


.08 696 


43 


40 


.08 699 


2580 


43 


56 


60 


.09718 


43 


40 


.09 721 


2640 


44 


56 


60 


.10716 


43 


40 


.10720 


2700 


45 


4.685 56 


60 


8.1 1 692 


5-31444 


40 


8. 1 1 696 


2760 


46 


56 


60 


.12647 


44 


40 


.12651 


2820 


47 


56 


60 


.13581 


44 


40 


•13585 


2880 


48 


56 


60 


.14495 


44 


39 


.14499 


2940 


49 


56 


66 


•15390 


44 


39 


•15395 


3000 


50 


4.685 56 


66 


8.16268 


5-31444 


39 


8.16272 


1 3060 


51 


56 


66 


.17 128 


44 


39 


•17 133 


: 3120 


52 


55 


61 


.17971 


44 


39 


• 17 976 


3180 


53 


56 


61 


.18798 


44 


39 


.18 803 


3240 


54 


5§ 


61 


.19610 


44 


39 


.19615 


3300 


55 


4.685 55 


61 


8.20 407 


5-31444: : 


39 


8.20412 


3360 


56 


55 


61 


.21 189 


44 


38 


.21 195 


i 3420 


57 


55 


61 


.21958 


44 


38 


.21 964 


; 3480 


58 


55 


61 


•22713 


44 


38 


.22719 


: 3540 


.J9__ 


55 


62 


•23455 


44 


38 


.23 462 



24 



TARLE III. 



I 


log sin (p = log 0" -|- S. 




V 


log 4 


) ' = log 


sin -f- S'. 




log tan <p = log 0-1-7". 




log (f. 


> ' = log 


tan 0-1- 7". 




// 


/ 


S 


T 


Log. Sin. 


S' 


T' 


Log-. Tan. 




3600 





4.685 5§ 


62 


8.24 i8§ 


5-31444 


38 


8.24 192 




3660 


I 


55 


62 


• 24 903 


45 


38 


.24910 




3720 


2 


55 


62 


.25 609 


45 


38 


•25 6ig 




3780 


3 


55 


62 


.26 304 


45 


3? 


.26311 




3840 


4 


55 


62 


.26 9S8 


45 


37 


.26995 ' 




3900 


5 


4.685 55 


62 


8.27 661 


5-3I445 


3? 


8.27 669 




3960 


6 


55 


63 


.28 324 


45 


37 


.28 332 




4020 


7 


54 


63 


.2897? 


4§ 


37 


.28985 




4080 


8 


54 


63 


.29620 


4§ 


37 


.29629 




4140 


9 


54 


63 


.30254 


4§ 


36 


■30 263 




4200 


10 


4.685 si 


63 


8.30879 


5-3I44? 


36 


8.30888 




4260 


1 1 


54 


63 


■3' 49§ 


4S 


36 


.31 504 




4320 


12 


54 


64 


.32 102 


4§ 


36 


.32 112 




4380 


13 


54 


64 


.32 701 


46 


36 


.32711 




4440 


14 


54 


64 


•33 292 


46 


36 


•33 302 




4500 


15 


4.685 54 


64 


8.3387s 


5.31446 


35 


8.33 885 




4560 


16 


54 


64 


.34450 


46 


3§ 


.34461 




4620 


17 


54 


65 


.35018 


46 


35 


.35029 




4680 


18 


54 


65 


.35 578 


46 


35 


•35 589 




4740 


19 


53 


65 


.36131 


46 


35 


.36 143 




4800 


20 


4.685 53 


6§ 


8.36677 


5.31446 


34 


8.36 689 




4860 


21 


53 


6§ 


.37217 


46 


34 


.37 229 




4920 


22 


53 


6? 


•37750 


46 


34 


•37 762 




4980 


23 


53 


66 


.38 276 


46 


34 


.38 289 




5040 


24 


53 


66 


•38 796 


47 


34 


.38 809 




5100 


25 


4.685 53 


66 


8.39 310 


5-31447 


33 


8.39323 




5160 


26 


53 


66 


.39818 


47 


33 


•3983? ! 




5220 


27 


53 


67 


•40 320 


47 


33 


•40 334 




52S0 


28 


52 


67 


.40816 


4? 


33 


.40 836 




5340 


29 


52 


67 


.41 307 


Al 


33 


.41 321 




5400 


30 


4.685 52 


6? 


8.41 792 


5-31447 


32 


8.41 807 




5460 


31 


52 


6? 


.42 271 


Al 


32 


.42 287 j 




5520 


32 


52 


68 


.42 746 


47 


32 


.42 762 




5580 


33 


52 


68 


•4321! 


48 


32 


.43 231 




5640 


34 


52 


68 


.43 680 


48 


31 


.43 696 




5700 


35 


4.685 52 


68 


8.44139 


5.31448 


31 


8.44156 




5760 


36 


52 


69 


•44 594 


48 


31 


.44611 




5820 


37 


51 


69 


•45 044 


48 


31 


.45 061 




5880 


38 


51 


69 


•45 489 


48 


30 


.45 507 




5940 


39 


51 


69 


•45 930 


48 


30 


•45 948 




6000 


40 


4.685 51 


69 


8.46 366 


5.31448 


30 


8.46 385 




6060 


41 


51 


70 


•46 798 


49 


30 


.46817 




6120 


42 


51 


70 


.47 226 


49 


30 


•47 24§ 




6180 


43 


51 


76 


•47 650 


49 


29 


.47 669 




6240 


44 


51 


76 


.48 069 


49 


29 


.48 089 I 




6300 


45 


4.685 56 


71 


8.48 485 


5-31449 


29 


8.48 505 j 




6360 


46 


50 


71 


.48 896 


49 


28 


.48917 




6420 


47 


50 


71 


•49 304 


49 


28 


•49 325 




6480 


48 


50 


72 


.49 708 


49 


28 


•49 729 




6540 


49 


50 


72 


.50 108 


50 


28 


.50130 I 




6600 


50 


4.685 50 


72 


8.50504 a 


5-31450 


2? 


8.50 526 




6660 


51 


50 


72 


.5089? 


50 


2? 


,50920 




6720 


52 


50 


73 


.51 286 


50 


27 


.51 310 




6780 


53 


49 


73 


.51672 


50 


27 


.51 696 




6840 


54 


49 


73 


.52055 


50 


2g 


.52079 




6900 


55 


4.685 49 


73 


8.52 434 


5-31450 


26 


8.52458 




6960 


56 


49 


74 


.52 810 


51 


26 


.52835 




7020 


57 


49 


74 


•53 183 


51 


25 


• 53 208 




7080 


58 


49 


74 


•53552 


51 


2§ 


•53578 1 




7140 


59 


49 


75 


•53918 


51 


25 


.53 944 1 



25 



TABLE III. 



1 log sin (p = log <p" -\- S. 




2° 


log (p 


" = log 


sin + ^'. 


log tan = log (p" -\- T. 




log (p 


" = log 


tan 0+ T. 


n 


/ 


S 


T 


Log'. Sin. 


S' 


T 


Log. Tan. 


i 72^ 





4.685 48 


75 


8.54282 


5-31451 


25 


8-54 308 


7260 


I 


48 


7§ 


.54642 


51 


24 


.54 669 


7320 


2 


48 


75 


.54 999 


51 


24 


.55027 


7380 


3 


48 


76 


.55354 


52 


24 


.55381 


i 7440 


4 


48 


76 


.5570? 


52 


23 


.55733 


7500 


5 


4.685 48 


76 


8.56054 


5.31452 


23 


8.56083 


7560 


6 


48 


11 


.56400 


52 


23 


.56429 


7620 


7 


4? 


11 


.56 743 


52 


'>2 


.56772 


7680 


8 


a1 


11 


.57 083 


52 


22 


.57 113 


7740 


9 


\1 


78 


.57421 


52 


22 


.57452 


i 7800 


10 


4.68547 


78 


8-57 756 


5.31453 


22 


8.57787 


! 7860 


II 


47 


78 


.58 089 


53 


21 


.58 121 


7920 


12 


47 


79 


.58419 


53 


21 


.58451 


7980 


13 


46 


79 


•58 747 


53 


21 


.58779 


8040 


14 


46 


79 


.59072 


53 


20 


•59 105 


1 8100 


15 


4.685 46 


80 


8.59395 


5.31453 


20 


8.59428 


I 8160 


16 


46 


80 


•59715 


54 


20 


.59749 


8220 


17 


46 


80 


.60 033 


54 


19 


.60 067 


8280 


18 


46 


81 


.60 349 


54 


19 


.60 384 


8340 


19 


4§ 


81 


.60 662 


54 


19 


.60 698 


8400 


20 


4.685 4§ 


81 


8.60 973 


5.31454 


18 


8.61 009 


8460 


21 


4! 


82 


.61 282 


54 


18 


.61 319 


8520 


22 


45 


82 


.61 589 


55 


18 


.61 626 


8580 


23 


45 


82 


.61 893 


55 


I? 


.61 931 


8640 


24 


45 


83 


.62 196 


55 


17 


.62 234 


8700 


25 


4.685 44 


83 


8.62 496 


5-31455 


16 


8.62 535 


1 8760 


26 


44 


83 


.62 795 


5! 


16 


.62 834 


i 8820 


27 


44 


84 


•63 091 


55 


16 


.63131 


8880 


28 


44 


84 


.63 385 


56 


15 


.63425 


; 8940 


29 


44 


84 


.63 67? 


56 


15 


.63718 


9000 


30 


4.685 43 


85 


8.63 968 


5-314 56 


15 


8.64 009 


! 9060 


31 


43 


8§ 


.64 2 56 


56 


14 


.64 298 


1 9120 


32 


43 


86 


.64 543 


56 


14 


.64 585 


9180 


33 


43 


86 


.64 827 


57 


14 


,64 870 


: 9240 


34 


43 


86 


.65 1 10 


57 


13 


•65153 


1 9300 


35 


4.685 43 


87 


8.65 391 


5-31457 


13 


8.65435 


i 9360 


36 


42 


%1 


.65 670 


5? 


12 


.65715 


9420 


37 


42 


%1 


.65 947 


Il 


12 


.65 993 


9480 


38 


42 


88 


.66 223 


58 


12 


.66 269 


9540 


39 


42 


88 


.66 497 


58 


II 


.66 543 


9600 


40 


4.685 42 


89 


8.66 769 


5-31458 


II 


8.66816 1 


! 9660 


41 


4? 


89 


.67 039 


58 


10 


.67 087 


9720 


42 


41 


89 


■67 308 


58 


10 


.67 356 


9780 


43 


41 


90 


.67 575 


59 


10 


.67 624 


9840 


44 


41 


90 


.67 840 


59 


09 


.67 890 


9900 


45 


4.685 41 


91 


8.68 104 


5-31459 


09 


8.68154 


9960 


46 


40 


91 


.68 366 


59 


08 


.68417 


: 10020 


47 


40 


91 


.68 627 


59 


08 


.68 678 


10080 


48 


40 


92 


.68 886 


60 


08 


.68 938 


IOI40 


49 


40 


92 


.69144 


60 


0I 


.69 196 


10200 


50 


4.685 40 


93 


8.69 400 


5.31460 


07 


8.69453 


10260 


51 


39 


93 


.69654 


60 


06 


.69 708 


j 10320 


52 


39 


93 


•69 90? 


60 


06 


.69 961 


10380 


53 


39 


94 


.70159 


61 


06 


.70 214 


10440 


54 


39 


94 


.70 409 


61 


05 


.70 464 


10500 


55 


4.685 38 


95 


8.7065^ 


5.31461 


05 


8.70714 


10560 


56 


38 


9§ 


.70 905 


61 


04 


.70 962 


1 10620 


57 


38 


96 


.71 150 


61 


04 


.71 208 


1 10680 


58 


38 


96 


.71 395 


62 


03 


•71 453 


j 10740 


59 


38 


97 


.71638 


62 


03 


.71 697 



26 



TABLE IV. 



Logarithmic Sines and Tangents 

Of all Angles from o° to 90° 

AT INTERVALS OF l'. 









0° 




TABLE IV. 


/ 


Log. Sin. 


D 


Log. Tan. 


Com. D. 


Log. Cot. 


Log. Cos. 







— CO 




— CO 




-L 00 


0.00000 


GO 


I 


6.46372 




6.46 372 




3-5362? 


0.00000 


59 


2 


6.7647! 


30103 
17609 


6.76475 


30103 


3-23 524 


0.00000 


58 


3 


6.94 084 


6.94084 


17609 


3-05915 


0.00000 


57 


4 


7.06 578 


12494 
9691 


7.06 578 


12494 
9691 


2.93421 


0. 00 000 


56 

55 


5 


7.16 269 


7.16 269 


2.83736 


0.00000 


6 


7.2418? 


6695 


7.24188 


79' 8 
6694 


2.75812 


0.00000 


54 


j 7 


7.30882 


7.30882 


2.69 1x7 


0.00 GOO 


53 


1 8 


7.36681 


5799 


7.36681 


5799 


2.63 318 


0.00000 


52 


9 


7.41 797 


5"5 
4575 
4139 


7.41 797 


5115 
4575 
4139 


2.58 203 


0.00000 


51 


10 

II 


7.46372 
7.50512 


7.46372 
7.50512 


2.53627 
2.49488 


0.00 000 
0.00000 


oO 

49 


12 


7.54290 




7.54291 


3779 


2.45 709 


9.99999 


48 


13 


7.57767 


3476 


7.57767 


3476 


2.42 233 


9.99999 


47 


H 


7.60985 


3218 
2996 

2S03 
2633 


7.60985 


3218 
2996 
2803 


2.39014 


9.99 999 


46 


1 15 


7.63981 


7.63982 


2.36018 


9-99 999 


45 


i6 


7.66784 


7.66785 


2.33215 


9.99999 


44 


i ^7 


7.69417 


7.69418 


2633 


2.30582 


9.99999 


43 


i8 


7.71 899 




7.71 900 




2.28 099 


9.99999 


42 


- 19 


7.74248 


2348 
2227 


7-74 248 


2348 
2227 


2.25751 


9.99999 


41 


20 


7.76475 


7.76476 


2.23524 


9.99999 


40 


21 


7.78 594 


^ 


7-78 595 


2119 


2.21 405 


9.99999 


39 


22 


7.80614 


, 


7.80615 




2.19384 


9.99999 


38 


! 23 


7.82 545 


1930 


7.82 546 


1930 


2.17454 


9.99999 


yi 


24 


7.84393 


1843 
1772 


7-84394 


1848 
1773 


2.15 605 


9.99999 


36 


25 


7.86 166 


7.86 16? 


2.13832 


9.99999 


35 


26 


7.87869 


1639 


7.87871 


1639 


2.12 129 


9-99 999 


34 


27 


7-89508 


7.89510 


2.10490 


9-99 998 


33 


' 28 


7.91088 


1579 


7.91 089 


1579 


2.08 910 


9-99 998 


32 


j 29 


7.92612 


1524 
1472 
1424 


7.92613 


1524 
1472 
1424 


2.07 386 


9-99 998 


31 


30 


7.94084 


7.94086 


2.05 914 


9-99 998 


30 


1 ^^ 


7.95 508 


7.95510 


2.04 490 


9.99998 


29 


32 


7.96887 


1379 


7.96 8S9 


1379 


2.03 III 


9.99998 


28 


33 


7.98223 


1336 


7.98225 


1336 


2.01 774 


9.99998 


27 


' 34 


7.99 520 


1296 


7.99 522 


1296 


2.00478 


9.99998 


26 


1 35 


8.00 778 




8.00781 




1.99 219 


9-99 997 


25 


36 


8.02 002 


1 190 
1158 
1128 
1099 
1072 


8.02 004 


1190 
1158 


1-97 995 


9.99997 


24 


37 


8.03 192 


8.03 194 


1.96805 


9.9999? 


23 


38 


8.04 350 


8.04 352 


1.95 64? 


9.99997 


n'y 


1 39 


8.05478 


8.05481 


1099 
1072 


1-94 519 


9-99 997 


21 


40 


8.06 57? 


8.06 580 


1.93 419 


9.99997 


20 


41 


8.07 650 


I046 


8.07653 




1.92 347 


9.99997 


19 


! 42 


8.08 696 


8.08 699 




1. 91 300 


9.99997 


18 


I 43 


8.09 718 


998 
976 


8.09721 




1.90278 


9-99 996 


17 


! 44 


8.10716 


8.10720 


999 
976 


1.89279 


9-99 996 


16 


1 "^5 


8. 1 1 692 


8. 1 1 695 


1.88303 


9-99 996 


15 


f 46 


8.12647 




8.12651 


954 


1.87349 


9.99996 


14 


47 


8.13 581 


934 


8.13585 


934 


1. 86415 


9.99996 


13 


1 48 


8.14495 


914 
895 
877 

860 


8.14499 


914 


1.85 506 


9.99996 


12 


1 49 


8. 1 5 390 


8.15395 


895 
877 

860 


1.84605 


9-99 995 


II 


50 


8.16268 


8.16272 


1.8372? 


9-99 995 


10" 


51 


8.17 128 


843 


8.17 133 


843 
827 


1.82 867 


9-99 995 


9 


52 


8.17 971 


827 
8ii 

797 

782 

763 


8.17 976 


1.82 023 


9-99 995 


8 


53 


8.18798 


8.18803 


1. 81 196 


9-99 995 


7 


54 


8.19610 


8.19615 


812 

797 
783 
768 


1.80384 


9-99 994 
9-99 994 


6 


55 


8.20407 


8.20412 


1.79587 


5 


56 


8.21 189 


8.21 195 


1.78804 


9.99994 


4 


57 


8.21958 


8.21 964 


1.78036 


9-99 994 


3 


58 


8.22713 


755 


8.22 719 


755 


1.77 280 


9.99994 


2 


59 


8.23455 


742 
730 


8.23462 


742 
730 


1.76538 


9-99 993 


I 


60 


8.24185 


8.24 192 


1.75808 


9-99 993 





! 


Log. Cos. 


D 


Log. Cot. 


Cora. D. 


Log. Tan. 


Log. Sin. 


' 



89^ 



28 



TABLE 


IV. 






r 








/ 


Loff. Sin. 


1) 


Ldi;. Tun. 


(Dm. I). 


Lor. Cot. 


Loir. Cos. 







8.24 i8§ 


7lS 


8.24 192 


718 


1.75808 


9-99 993 


60 


I 


8.24903 


706 


8.24910 




1.75090 


9-99 993 


59 ; 


'y 


8.25 609 


8.25 616 


695 


1.74383 


9-99 993 


58 


3 


8.26304 




8.26311 


1.73688 


9.99992 


57 


4 


8.26988 


673 


8.26995 


673 
663 


1.73004 


9.99992 


56 ! 


5 


8.27661 


8.27669 


1.72331 


9.99992 


55 


6 


8.28324 




8.28332 


1. 71 667 


9.99992 


54 


7 


8.2897? 


653 


8.28985 


653 


I. 71 014 


9-99992 


53 


: 8 


8.29 626 


643 


8.29629 


643 


1.70 371 


9-99 99' 


52 


9 


8.30254 


634 
625 


8.30263 


634 
625 

616 


1.69736 


9.99991 


51 


10 


8.30879 


8.30888 


1.69 III 


9.99991 


50 


II 


8.31495 




8.31 504 


607 


1.68495 


9.99990 


49 


12 


8.32 102 




8.32 112 


1.67888 


9.99990 


48 


' 13 


8.32701 


599 


8.327II 


599 


1.67288 


9.99990 


47 


u 


8.33292 


591 

583 


8.33302 


591 

583 


1.6669? 


9.99990 


46 


15 


8.33875 


8.33885 


1.66 114 


9.99989 


45 


i6 


8.34450 


575 


8.34461 


568 


1.65 539 


9.99989 


44 


^7 


8.35018 


567 


8.35029 


1.64971 


9.99989 


43 


i8 


8-35 578 


560 


8.35 589 


560 


1.64 410 


9-99989 


42 


19 


8.36 131 


553 
546 


8.36 143 


553 
546 


1.63857 


9.99988 


41 


L'O 


• 8.36677 


8.36689 


1.63 316 


9.99988 


40 


21 


8.37217 


539 


8.37 229 




1.62 771 


9.99988 


39 


'T^ 


8.37750 


533 


8.37762 




1.62238 


9.9998? 


38 


23 


8.38276 


526 


8.38289 


527 


1. 61 711 


9.9998? 


37 


24 


8.38796 


520 
514 


8.38809 


520 

514 
508 


1. 61 191 


9.99987 


36 


-5 


8.39310 


8.39323 


1.60676 


9-99986 


35 


26 


8.39818 




8.39 83? 


1.60 168 


9-99986 


34 


27 


8.40 320 


502 


8.40 334 




1.59666 


9.99986 


33 


28 


8.40816 


496 


8.40 830 


496 


1.59 169 


9.99986 


32 


29 


8.41 307 


491 
485 


8.41 321 


491 
485 
480 


1.58678 


9.99985 


31 


30 


8.41 792 


8.41 807 


1.58 193 


9.99985 


30 


31 


8.42 271 


479 


8.42287 


1.57713 


9.99985 


29 


32 


8.42 746 


474 


8.42 762 




1.57238 


9.99984 


28 


33 


843215 


469 


8.43231 


469 


1.56768 


9.99984 


27 


34 


8.43 680 


464 
459 


8.43 696 


464 
460 


1.56304 


9.99984 


26 


35 


8.44 139 


8.44 156 


1.55844 


9-99983 


25 


36 


8.44 594 




8.44 61 1 




1.55389 


9-99983 


24 


37 


8.45 044 


450 


8.45 061 




1.54 938 


9.99982 


23 


3S 


8.45 489 


445 


8.45 507 




1.54493 


9.99982 


22 


39 


8.45930 


440 
436 


8.45 948 


441 
437 


1.54052 


9.99982 


21 


40 


8.46 366 


8.46 385 


1-53615 


9.99981 


20 


41 


8.46 798 


428 


8.46817 




1-53183 


9.9998! 


19 


42 


8.47 226 


8.47 245 


423 


1.52754 


9.99981 


18 


43 


8.47 650 


423 


8.47 669 




1.52330 


9.99980 


17 


44 


8.48069 


419 
415 


8.48089 


,419 
416 


1.51911 


9.99980 


16 


45 


8.48485 


8.48 505 


1. 51 495 


9.99979 


15 


46 


8.48 896 




8.48917 


408 


1. 51 083 


9-99 979 


14 


! 47 


8.49304 




8.49325 


1.50675 


9-99 979 


13 


48 


8.49 708 


404 


8.49 729 




1.50270 


9-99 978 


12 


49 


8.50108 


400 
396 


8.50 130 


400 
396 


1.49 870 


9.99978 


II 


50 


8. 50 504 


8.50526 


1.49473 


9-99978 


10 


51 


8.50897 


393 


8.50920 


393 


1.49080 


9.9997? 


9 


52 


8.51286 


389 


8.51 310 




1.48 690 


9.99977 


8 


53 


8.51672 


386 


8.51 696 




1.48 304 


9-99 976 


7 


54 


8.52055 


382 
379 


8.52079 


383 
379 


1.47 921 


9.99976 


6 


55 


8.52434 


8.52458 


1.47 541 


9-99 975 


5 


56 


8.52810 




8.52835 




1-47 165 


9-99 975 


4 


57 


8.53183 


373 


8.53208 




1.46792 


9-99 975 


3 


58 


8.53552 


369 


8.53578 




1.46422 


9.99974 


2 


59 


8.53 918 


363 


8. 53 944 


366 
364 


1.46055 


9-99 974 


I 


60 


8.54282 


8. 54 308 


1.45 691 


9-99 973 







Los. Cos. 


D 


Log. Cot. 


Cora. D. 


Log. Tan. 


Log. Sin. 


/ 



88^ 



29 



TABLE 


IV. 




2° 




TABLE IV. 


/ 


Log. Sill. 


D 


Log. Tan. 


Com. D. I 


og. Cot. 


Log. Cor. 


' 





8.54282 


360 


8.54 3O8 


360 J 
358 J 


.45691 


9-99 973 


60 


I 


8.54642 


8.54669 


-45331 


9-99 973 


59 


2 


8.54999 




8.55027 


• 44 973 


9.99972 


58 


3 


8-55 354 


354 


8.55381 


354 J 


-44618 


9.99972 


57 


4 


8.55705 


351 
348 
346 


8-55 733 


352 I 


44266 


9.99971 


56 


5 


8.56054 


8.56083 


349 

346 J 


43917 


9.99971 


55 


6 


8. 56 400 


8.56429 


43571 


9.99971 


54 


7 


8.56743 


343 


8.56775 


343 I 


43227 


9.99970 


53 


8 


8.57083 


340 


8-57 113 


341 I 


42886 


9.99970 


52 


9 


8. 57 421 


338 
335 


8.57452 


338 I 


42548 


9.99969 


51 


10 


8.57 756 


8.57787 


3Ji . 


42 212 


9.99969 


50 


II 


8.58089 




8.58 121 


333 J 


41 879 


9.99968 


49 


12 


8.58419 




8.5845? 


33° J 


41 548 


9.99968 


48 


13 


8.58747 


327 


8.58779 


328 J 


41 220 


9.99967 


47 


14 


8.59072 


325 
323 


8.59105 
8-59 428 


325 I 


40895 


9.99967 
9.99966 


46 


15 


8.59395 


323 J 


40571 


45 


i6 


8.59715 




8.59749 


320 J 


40251 


9.99966 


44 


17 


8.60033 


3'8 


8.6006^ 


318 I 


39932 


9.99965 


43 


i8 


8.60349 


316 


8.60384 


316 I 


39616 


9.99965 


42 


19 


8.60662 


313 
3>i 


8.60 698 


314 I 


39302 


9.99964 


41 


20 


8.60973 


8.61 009 


"*" '"'l 


38990 


9.99964 , 


40 


21 


8.61 282 




8.61 319 


309 J 


38681 


9.99963 


39 


22 


8.61 589 


306 


8.61 626 


307 I 


38374 


9.99963 


38 


23 


8.61 893 


304 


8.61 931 


305 I 


38068 


9.99962 


37 


24 


8.62 196 


302 
300 


8.62 234 


303 I 


37765 


9.99962 


36 


25 


8.62 496 


8-62 535 


300 J 


37465 


9.99.961 


35 


26 


8.62795 


298 


8.62 834 


299 J 


37 166 


9.99961 


34 


27 


8.63091 


296 


8-63 131 


297 I 


36869 


9.99960 


33 


28 


8.63 38S 


294 


8-63425 


294 I 


36574 


9-99 959 


32 


29 


8.6367^ 


292 
290 

288 


8.63 718 


293 I 


36281 


9-99 959 


31 


30 


8.63968 


8.64009 


2yi 


35990 


9-99 958 


30 


31 


8.64256 


8.64298 


288 J 


35702 


9.99958 


29 


32 


8.64 543 


286 


8.64 585 


287 J 


35414 


9-99 957 


28 


33 


8.6482^ 


284 


8.64870 


28s J 


35 129 


9-99 957 


27 


34 


8.65 no 


282 
281 


8.65153 


283 I 


34846 


9-99 956 


26 


35 


8.65 391 


8.65435 


281 


34565 


9.99956 


25 


36 


8.65 670 




8.65715 




34285 


9-99 95§ 


24 


37 


8.6594? 


277 


8.65 993 


278 J 


34007 


9-99 954 


23 


38 


8.66223 


275 


8.66 269 


276 J 


33731 


9-99 954 


22 


39 


8.66497 


274 
272 


8.66 543 


274 I 


33 456 


9-99 953 


21 


40 


8.66769 


8.66816 




33184 


9-99 953 


20 


41 


8.67 039 


26§ 


8.67087 


269 


32913 


9.99952 


19 


42 


8.67 308 


8-67 356 


32643 


9.99952 


18 


43 


8.67 575 




8.67 624 




32376 


9.99951 


17 


44 


8.67 846 


265 
264 
262 


8.67 890 


266 , 


32 no 


9-99950 


16 


45 


8.68 104 


8.68 154 




31845 


9.99950 


15 


46 


8.68 366 


^8.68417 




31583 


9-99 949 


14 


47 


8.68627 




8.68 678 




31 321 


9-99 948 


13 


48 


8.68 886 


259 


8.68938 


259 J 


31 062 


9.99948 


12 


49 


8.69 144 


257 
256 


8.69 196 


258 I 


30 803 


9-99 947 


II 


50 


8.69 400 


8.69453 


■■^bb - 


30547 


9-99 947 


10 


51 


8.69654 


254 


8.69708 


255 J 


30292 


9-99 946 


9 


52 


8.6990^ 


253 


8.69 961 


253 J 


30038 


9-99 945 


8 


53 


8.70159 


251 


8.70214 




29786 


9-99 945 


7 


54 


8. 70 409 


250 
248 


8.70464 


250 J 


29535 


9.99944 


6 


55 


8.70657 


8.70714 


249 

248 


29286 


9-99 943 


5 


56 


8.70905 




8.70962 


29038 


9-99 943 


4 


57 


8.71 150 


245 


8.71 208 


246 , 


28 791 


9.99942 


3 


58 


8.71 395 


244 


8.71453 


245 J 


28546 


9.99942 


2 


57 


8.71 638 


243 
241 


8.71 697 


243 J 


28303 


9.99941 


I 


60 


8.71 880 


8.71 939 


^4.! 


28 066 


9-99940 







Log. Cos. 


D 


Log. Cot. 


Com. D. L( 


)g. Tan. 


Log. Sin. 


/ 



87 



30 



TABLE IV. 



Lour. Sin. 



c. d. 



I.os. Tail. 



oif. Cot. 



liOu'. Cos. 



10 

II 

12 
13 
1± 
15 
16 

17 
18 

19 



21 

22 

24 



25 
26 
27 
28 
29 

30 

31 

32 
33 
34 



35 
36 
37 
38 
39 



40 

41 
42 
43 
44 



45 
46 

47 
48 

49 

50 

51 
52 

53 

54 

55 
56 
57 
58 
59 



8.71 880 

8.72 120 

8.72359 
8.72597 
8.72833 



8.73069 
8.73 302 
8.73 53? 
8.73766 
8. 73 997 



8.74 226 

8.74453 
8.74680 

8.7490! 

8.75 129 

8-75 353 
8.75574 

8.75795 
8.76015 
8.76233 



8.76451 
8.7666^ 
8.76883 
8.77097 
8.77310 



8.77522 
8.77733 
8.77943 
8.78 152 
8.78360 



8.78 567 
8.78773 
8.78978 
8.79183 
8.79386 



8.79 588 

8.79789 
8.79989 
8.80189 
8.80387 



8.80 585 
8.80782 
8.80977 

8.81 172 
8.81 366 
8.81 560 
8.81 752 

8.81 943 

8.82 134 
8.82324 



8.82 513 
8.82 701 
8.82888 
8.83075 
8.83260 



8.8344? 
8.83629 
8.83813 
8.8399? 
8.8417? 



60 



8.84358 
Log. Cos. 



240 
239 
237 

236 
235 
233 
233 
231 
230 
22g 
227 

226 

225 
224 
223 

221 
221 
219 

218 
217 

216 
2I§ 
214 
213 
213 
211 
210 
209 
208 
207 
206 
205 
204 
203 
202 
201 
200 
199 

'98 
197 

197 
19s 
195 
194 
193 
192 
191 
191 



187 
186 
185 
185 
184 
183 
182 
182 
181 



8.71 939 

8.72 180 
8.72426 
8.72 659 
8.72896 



8.73 131 
8.73366 

8.73 599 
8.73 83? 
8.74062 



8.74292 

8. 74 520 
8.74748 
8.74974 

5.75 199 



8.75422 

8.7564? 
8.75867 
8.76087 
8.76 306 



8.76524 
8.76741 
8.76958 
8.77 172 
8.77 386 



8.77 599 
8.77811 
8.78022 
8.78232 
8.78441 



8.78648 
8.78855 
8.79061 
8.79 266 
8.79470 



8.79673 

8.79875 
8.80075 

8.80276 
8.80476 



8.80 674 
8.80871 

8.81 068 
8.81 264 
8.81 459 



8.81 653 

8.81 846 
8.82038 

8.82 230 
8.82420 



8.82616 
8.82799 
8.82987 

8.83175 
8.83 361 



8.83547 
8.83732 

8.83 916 

8.84 100 
8.84282 
04"46f 
Log, Cot. 



241 

240 

238 
237 

235 
23s 
233 
232 
231 
229 

22§ 
227 
226 
225 
223 
223 
221 
220 
219 
21S 
217 

216 
214 
214 
213 
212 
210 
210 
209 
207 
207 
206 
204 
204 
203 
202 
201 
200 
199 
198 
197 
197 
195 
195 
194 

193 
192 
191 
190 
190 



187 

iSg 

185 



Ib2 
182 

"cTdT 



28 066 
27 819 
27 579 
27341 
27 104 



26 868 
26633 
26406 
26 163 
2593? 



25 708 

25479 
25252 
25 026 
24 801 



24577 
24354 
24133 
23913 
23693 



2347? 
23258 
23 042 
22 82? 
22 613 



22 400 
22 188 
21 978 
21 768 
21 559 
21 351 
21 144 
20 938 
20734 
20530 



9 326 

9 128 

931 
8736 
8541 



9.99940 
9.99940 
9-99 939 
9-99 938 
9.99938 



9.99937 
9-99 936 
9-99 93? 
9-99 935 
9-99 934 

9-99 933 
9-99 933 
9-99 932 
9-99931 
9-99931 



9.99 930 
9.99929 

9.99928 
9.99928 
9.99927 



9.99926 
9-9992? 
9-99925 
9-99 924 
9-99923 
9.99922 
9.99922 
9.99921 
9.99920 
9.99919 



9.99919 
9.99918 
9.9991? 

9-99 916 
9.99916 



<>0 

59 
58 
57 
_5^ 
55 
54 
53 
52 
51 
50 
49 
48 
47 

45 
44 
43 
42 
41 
40 
39 
38 
37 
_3^ 

35 
34 
33 
32 

Jl 
30 

29 
28 
27 
26 



9.99915 
9.99914 

9-99913 
9.99912 
9.99912 



9-99 911 
9.99910 
9.99 909 
9.99 908 
9-9990? 



25 
24 

23 
22 
21 

"20 

19 
18 

17 
16 



9-99 907 
9-99906 
9-99 90? 
9.99904 

9-99903 



5 53? 

Log. Tan, 



9.99902 
9.99902 
9.99901 
9.99900 
9-99899 
9.99898 
9-9989? 
9-99896 
9.99896 

9-99895 

9-99894 
Log, 8iu. 



15 
14 
13 
12 
II 

lo 

9 

8 

7 
6 





330 


320 


310 


6 


33 


32.0 


310 


7 


38 


5 


37-3 


36.1 




44 





42-6 


4'-3 


9 


49 


5 


48.0 


46. S 


10 


55 





53-3 


S'-6 


20 


110 





106.6 


103 -3 


30 


lbs 





160.0 


155-0 


40 


220 





213-3 


206.^ 


SO 


275 





266.6 


258-3 





290 


280 


270 


6 


29.0 


28.0 


27.0 


7 
8 


33-8 
38.6 


32 
37 


6 
3 


36.0 


9 

10 


43-5 
48.3 


42 
46 




6 


40.5 
45° 


20 


96.6 


93 


3 


90.0 


30 
40 


145.0 
193-3 


140 
186 




6 


135-0 
180.0 


5'^ 


241-6 


233 


3 


225.0 



250 240 230 



24.0 

28.0 
32.0 
36.0 
40.0 

80.0 

120.0 
160.0 
200.0 





210 


200 


190 


6 


21 .0 


20.0 


iQ.ol 


7 
8 


24 
28 


5 



23-3 
26.6 


22 
25 


I 

3 


9 


31 


5 


30.0 


28 


5 


10 

20 


35 
70 






33-3 
66.6 


31 
63 


3 


30 


105 





lOO.O 


95 





40 
50 


140 
175 






166.6 


126 

158 


3 





9 


9 


8 


7 


6 


a 


6 


0.9 


0.9 


0.8 


0.7 


0.6 


0. 


7 


I.I 


I 











8 





7 


0. 


8 


1.2 


I 


2 


I 





o.q 





8 





9 


1.4 


I 


3 


I 


2 


1 .0 





9 





10 


i.b 


I 


5 


I 


3 


1 . 1 


1 





0. 


20 


31 


3 





2 


6 


2-3 


2 





I . 


30 


4-7 


4 


5 


4 





3 5 


3 





2. 


40 


b-3 


6 





5 


3 


4 6 


4 





3- 


50 


7-9 


7 


5 


6 


6 


5-8 


5 





4- 



300 

30.0 
3S-0 
40.0 
45-0 
50.0 
100.0 
150.0 
200.0 
250.0 



260 

26.0 
30.3 
34-6 
390 
43-3 
86.6 
130.0 
173-3 
216.6 



220 

22.0 
25-6 

29-3 
33-0 
36.$ 

73-3 

IIO.O 

146.6 

183.3 



18.0 

21.0 
24.0 
27.0 
30.0 

60.0 
90.0 
120.0 
150.0 





4 


4 


3 


2 


I 


i 


b 


0.4 


0.4 


0-3 


0.2 


0.1 





7 
8 


0-5 
0.6 


0.4 
0..5 






3 
4 






2 


i 






9 

10 


0.7 


o.b 

o-f, 






4 
5 





3 


0.1 
o.i 






20 


1-5 


'•3 


I 








6 


0-3 





30 


2.2 


2.0 


I 


5 


I 





o.S 





40 

50 


30 
3-7 


3-3 


2 
2 




5 


1 
I 


3 
6 


0-8 



0. 



p, p. 



86^ 



31 



TABLE IV. 



Log. Sill. 



Loff. Tan. c. d. 



Log. Cot. I Lost. Cos. 



10 

II 

12 
14 



15 
16 

18 
19 



20 

21 

22 

23 
24 



25 
26 

27 
28 

29 



30 

31 

32 
33 

34 



35 
36 
37 
38 
39 



40 

41 
42 
43 
44 



45 
46 

47 
48 

49 



50 

51 

52 
53 

54 

55 
56 
57 
58 
59 
60 



8.84 358 

8.84 538 
8.84718 
8.84897 

8.85075 

8.85 252 
8.85 429 
8.85605 
8.85780 
8.85954 



8.86128 
8.86 301 
8.86474 
8.86645 
8.86 816 



8.86987 
8.87156 
8.8732? 
8.87494 
8.87 661 



8.87828 
8.87995 
8.88 166 
8.88326 
8.88490 



8.88654 
8.8881? 
8.88980 
8.89 142 
8.89303 



8.89464 
8.89624 
8.89784 

8.89943 
8.90 loi 



8.90 259 
8.90417 
8.90573 
8.90729 
8.90885 



.91 040 
.91 195 

•91 349 
.91 502 
.91655 



.91 80? 
.91 959 
.92 1 16 
.92 261 
.92 411 



.92 561 
.92 710 
.92858 
.93007 
•93 154 



8.93 301 
8.93448 

8-93 594 
8.93740 
8.93885 



8.94029 

Log. Cos. 



8.84464 
8.84645 
8.84826 
8.85005 
8.85 184 



8.85363 
8.85 546 

8.85717 
8.85893 
8.86068 



8.86 243 
8.8641? 
8.86590 
8.86763 
8.86935 



8.87 log 
8.87277 
8.87447 
8.87616 
8.87 785 



8.87953 
8.88 120 
8.88287 
8.88453 
8.88 618 



8.88783 
8.8894? 
8.89 III 
8.89274 
8.89436 



8.89 598 

8.89759 

8.89 926 
8.90086 

8.90 240 



8.90398 
8.90557 
8.90714; 
8.90872 

8.91 028 



8.91 184 

8.91 340 
8.91 495 
8.91 649 
8.91 803 



8.91 957 

8.92 109 
8.92 262 
8.92413 
8.92 565 



8.92715 
8.92866 
8.93015 
8.93 164 
8.93313 



8.93461 
8.93 609 
8 93 756 
8.93903 
8.94049 



8.94 195 



Log. Cot. c. d 



1-15535 

I-I5354 
1. 15 174 
1. 14 994 
1.14815 



1-14637 
1. 14459 
1. 14283 
1. 14 107 
1-13931 



I-I3756 
1. 13 582 
1 . 1 3 409 

1-13237 
1. 13065 



1.12893 
1. 12 723 

1-12553 
1. 12 384 
1. 12 215 



9.99894 

9-99893 
9.99892 
9.99891 
9.99896 



9.99889 
9-99888 
9.99888 
9.99887 
9.99 886 

9-99885 
9.99884 
9.99883 
9.99 882 
9.99 881 



1 . 1 2 047 
1. 1 1 880 
I. II 713 
1. 1 1 547 
I. II 381 



I. II 216 

I. II 052 
1. 10 889 
1. 10726 
1. 10 563 



1.10401 
1. 10 246 
1. 10079 
1.09 919 
1.09 760 



1.09 601 
1.09443 
1.09 285 
1.09 128 
I -08 971 



1.08 815 
1.08 660 
1.08 505 
1.08356 
1.08 196 



1.08 043 
1.07 896 
1.07 738 
1.07 586 
1-07435 



1.07 284 
1.07 134 
1.06 984 
1.06 835 
1.06686 



1.06 538 
1.06 396 
1.06 243 
1.06097 
1-05950 



9.99 886 
9.99879 

9-99878 
9.9987? 

9-99876 



9.99875 
9.99874 
9-99 874 
9-99873 
9.99872 



9.99871 
9.99870 
9.99869 
9.99868 
9.99867 



9.99 866 
9.99865 
9.99864 
9.99863 
9.99 862 



9.99 861 
9.99 860 
9.99859 
9-99858 
9.99857 



9.99856 
9.99855 

9-99853 
9.99852 
9.99851 



9.99856 
9.99849 
9.99848 
9.9984? 
9-99846 
9.99845 
9-99844 
9-99843 
9.99842 
9.99841 



9-99840 
9-99839 
9-9983? 
9-99836 
9-99 83? 



1.05 805 
Log. Tan. 

85^ 



9-99834 

Log. Sin. 



00 

59 
58 
57 

JL 
55 
54 
53 
52 
51 
50 

49 
48 

47 
46 

45 
44 
43 

42 

41 
40 

39 

38 

37 

_36_ 

35 
34 
33 
32 
31 
30 
29 
28 
27 
26 



25 
24 

23 
22 
21 

"20 

19 

18 

17 
16 



15 

14 
13 
12 
II 

lo 

9 

8 

7 
6 

5 
4 
3 
2 
I 

~0 





180 


177 


174 


17 


I 


6 


18.0 


17 7 


17.4 


17. I 


7 


21 .0 


20 


6 


20 


3 


19 


9 


8 


24.0 


2^ 


6 


23 


2 


22 


« 


9 


27.0 


26 


5 


26 


I 


25 


6 


10 


30.0 


29 


,S 


29 





28 


5 


20 


60.0 


';q 





ss 





,S7 





30 


90.0 


8S 


5 


»7 





»5 


5 


40 


120.0 


118 





lib 





114 





50 


150.0 


147 


5 


145 





142 


5 



168 

16 
19 

22 

25 
28 

56 



165 



162 

16. 



159 



1.37. s 135.0 132.5 





156 


153 


150 


14 


6 


VS.b 


15.3 


15.0 


14 


7 


18.2 


17 


8 


17 


5 


17 


8 


20.8 


20 


4 


20 





19 


9 


23-4 


22 


9 


22 


5 


22 


10 


26.0 


25 


5 


25 





24 


20 


52.0 


.SI 





so 





49 


30 


78.0 


76 


5 


75 





73 


40 


104.0 


102 





100 





98 


50 


130.0 


127 


5 


125 





122 



144 

14 
16 



p. p. 



32 



TABLE IV. 



5 
6 

7 
8 

9 

10 

II 

12 

13 

14 



15 
i6 

17 
i8 

19 



20 

21 

22 

23 

24 



-3 
26 
27 
28 
_29_ 

30 

31 
32 
33 

34 



35 
36 
37 
38 
39 



40 

41 
42 
43 

44 



45 
46 

47 
48 

49 
50 

5t 

52 
53 

54 



55 
56 
57 
58 
59 
60 



liOif. Sin. 
8.94029 
8.94 174 

8.94 3'7 
8. 94 460 
8.94603 



8.94745 
8.94887 
8.95028 
0.95 169 
S.95310 



8 95 450 

8.95 5S9 
8.95 728 
8.95867 
8.96005 



8.96 143 
8.96280 
8.96417 
8.96553 
8.96689 



8.96 825 

8.96 960 
8.97094 

8.97 229 
8.97363 



8.97496 
8.97 629 
8.97 762 
8.97 894 
8.98026 



8.98 157 
8.98 288 
8.98 419 

8. 98 549 
8.98679 



8.98 808 

8.9S93? 
8.99066 

8.99 194 
8-99 3^2 



8.99449 

8.99577 
8.99703 
8.99 830 
8.99956 



9.00081 
9.00 207 
9.00 332 
9.00456 
9.00 5S0 

9.00 704 
9.00828 

9.00 951 

9.01 073 
9.01 196 



9.01 318 
9.01 440 
9.01 561 
9.01 682 
9.01 803 

9.01 923 
Log. Cos. 



Log. Tail. I c. (1. I 
8.94 195 
8.94340 

8.94485 
8.94629 

8.94773 



8.94917 
8.95059 
8.95 202 

8.95 344 
8.9548? 



8.95626 
8.9576? 

8.95 90? 
8.9604? 

8.9 6 186 
8796"^ 
8.96464 
8.96602 
8.96739 
8.96876 



8.97 013 

8.97 149 
8.97285 
8.97421 
8.97 556 



8.97 696 
8.97825 

8.97 958 

8.98 092 
8.98 225 



8.98357 
8.98490 
8.98621 
8.98753 



8.99015 

8.99 145 
8.99275 
8.99404 
8-99 533 



8.99662 
8.99791 
8.99919 
9.00 046 
9.00 174 



9.00 300 
9.00427 
9.00553 
9.00 679 
9.00 804 



9.00930 
9.01 054 
9.01 179 
9.01 303 
9.01 427 



9.01 550 
9.01 673 
9.01 796 

9.01 918 

9.02 046 
9.02 162 
1,0?. Cot. 



c. d. 



iOg. Cot. 
.05 805 
.05 659 
.05 515 
.05 370 
.05 226 



.05 083 
.04 946 

.04 798 
,04656 
.04514 



.04 373 
.04232 
.04092 
•03952 
.03813 



.03674 
•03 536 
.03 398 
.03 260 
.03 123 



.02 986 
.02 850 
.02 714 
.02 579 
.02 444 



.02 309 
.02 175 
.02 041 
.01 908 
■01 775 



.01 642 
.01 510 
.01 378 
.01 247 
.01 1 16 



.00 985 
.00855 
.00 725 
.00 59§ 
. 00 466 



Loir. Cos. 



00337 
00 209 
00081 

0.99953 
0.99 826 



0.99699 

0.99 573 
0.99 446 
0.99321 
0.99 195 



0.99070 
0.98 94 § 
0.98821 
0.98 697 
0.98 573 



0.98 450 
0.98327 
0.98 204 
0.98 081 
0.97959 
0.97 838 

JiOg. Tan. 

84^ 



99 834 
99833 
99832 
99831 
99830 
99829 
9982? 
99826 
99825 
99824 

99823 
99 822 
99821 
99819 
99818 
9981? 
99816 
99815 
99814 
99813 



99 81 1 
99 816 
99 809 
99 808 
99807 



99805 
99 804 
99803 
99 802 
99801 



99799 

99 798 
99 797 
99796 

99 794 

99 793 
99792 
99791 
99789 
99788 



99787 
99786 
99784 

99783 
99782 



99781 
99779 
99 778 
99 777 
99776 



99 774 

99 773 
99772 

99770 
99769 



99768 

99766 
99765 
99764 
99763 



9-99761 

Log. Sin^ 



«0 

59 
58 
57 
56 



55 
54 
53 
52 
_51 
50 

49 
48 

47 
46 



45 
44 
43 
42 
41 
40 
39 
38 

yi 
36 



35 
34 
33 
32 
31 

30 

29 

28 

27 
26 



25 
24 

23 
22 
21 

"20 

19 

18 

17 
16 



15 
14 
13 
12 
II 

To 

9 

8 

7 
6 





MS 


144 


143 


142 


141 


6 


M-S 


14.4 


M-3 


14.2 


14 I 


7 


16.5 


16.8 


16.7 


16. .S 


16.4 


8 


I9-3 


19.2 


19.0 


18.9 


18.8 


9 


21.7 


21 .6 


21.4 


2>.3 


ai . I 


10 


24.1 


24.0 


2^-8 


23fi 


235 


20 


4«-3 


48.0 


47-6 


47-3 


47.0 


30 


72 5 


72.0 


71-5 


71.0 


70.5 


40 


9f> 5 


96.0 


95.? 


9^6 


94.0 


50 


120. g 120.0 


119. 1 


118. 3 117. 5 




140 


139 


138 


137 


136 



6 
7 


14.0 
16. q 


13 
16 


9 
2 


13 
16 


8 

I 


13 
16 


7 


8 


18.6 


18 


5 


18 


4 


18 


2 


9 


21.0 


20 


S 


20 


7 


20 


5 


10 
20 
30 


233 
46-6 
70.0 


23 
46 
69 


1 
3 

5 


23 

46 
69 







22 

45 
68 


8 
6 
5 


40 


93-3 


92 


6 


92 





91 


3 


50 


116. 6 


"5 


8 


"5 





114 


I 





135 


134 


133 


6 


13-5 


13-4 


13-3 


7 


15-7 


15-6 


15-5 


8 


18.0 


17-8 


17.7 


9 


20.2 


20. 1 


19.9 


10 


22.5 


22.3 


22.1 


20 


45.0 


44-6 


44-3 


30 


67-S 


67.0 


66.5 


40 


90.0 


89.3 


88.6 


50 


112. 5 


III. 6 


IIO.§ 





13 


I 


130 


129 


6 


13. 1 


13.0 


12 


9 


7 


15 


3 


15. 1 


15 





8 


17 


4 


17-3 


17 


2 


9 


19 


6 


I9-S 


19 


3 


10 


21 


8 


21.6 


21 


5 


20 


43 


6 


43-3 


43 





30 


bS 


S 


65.0 


64 


.5 


40 


«7 


3 


86.6 


86 





50 


109 


I 


108.3 


107 


5 



13.6 

is-8 
18.1 
20.4 

22.0 

45-3 
68.0 
9o.§ 
"3-3 



13.2 
15-4 
17.6 
19.8 
22.0 
44.0 
66.0 



128 

12.8 
14.9 
17.6 
19.2 
21.3 

42-6 
64.0 
85.§ 
106.6 



127 126 125 124 123 



6 


12 


7 


12 


6 


12 


S 


12.4 


7 


14 


8 


14 


7 


14 


6 


14.4 


8 


lb 


9 


16 


8 


16 


6 


16.. S 


9 


19 




18 


9 


18 


7 


18.6 


10 


21 


I 


21 





20 


8 


20.g 


20 


42 


3 


42 





41 


6 


41-3 


30 


63 


5 


63 





62 


S 


62.0 


40 


84 


6 


84 





B3 


3 


82.6 


50 


105 


8 


105 





104 


I 


103.3 



12.3 

14-3 
16.4 
18.4 
20.5 
41.0 
61.5 
82.0 
102.5 





122 


121 


120 


I 


I 


C 


6 


12.2 


12. 1 


12.0 


0.1 


0.1 





7 


14.2 


14.1 


14.0 


0.2 


0. 1 





8 


16.2 


16. i 


16.0 


0.2 


o.i 





9 


18.3 


18. 1 


18.0 


0. 2 


0.1 





10 


20.3 


20. 1 


20.0 


0.2 


o.i 





20 


40-6 


40.3 


40.0 


o.c; 


0.3 





30 


61.0 


60. s 


60.0 


0.7 


o.s 





40 


«i.3 


80.6 


80.0 


I.O 


6 





50 


101.6 


100. § 


100. 


1.2 


0.8 






P. p. 



33 



TABLE IV. 



10 

II 

12 
13 

H 

15 
16 

17 
18 

19 



20 

21 
22 

23 
24 



25 
26 



30 

31 
32 
33 
34 



35 
36 
37 



40 

41 

42 

43 
44 



45 
46 

47 
48 

49 



50 

51 

52 
53 
54 



55 
56 
57 
58 
59 
60 



Log. Sill. I d. 

9.01 923 

9.02 043 
9.02 163 
9.02 282 
9.02 40T 



9.02 520 
9.02 638 

9-02 756 
9.02 874 
9.02 992 



9.03 109 
9.03 225 

9-03 342 
9.03458 

9-03 574 



9.03689 

9.03 805 
9.03919 
9.04034 

9.04 148 



9.04 262 
9.04 376 
9.04489 
9.04 602 
9-04 71 g 



9.04828 
9.04940 
9.05 052 
9.05 163 
9.05275 



9.05 386 

9- 05 496 
9.05 607 
9.05717 
9.05 827 



9-05 936 
9.06046 
9.06155 
9.06 264 
9.06372 



9.06 486 
9.06 588 
9.06 696 
9.06 803 
9.06 916 



9.07 017 
9.07 124 
9.07 230 

9-07 336 
9.07 442 



9.07 548 
9.07653 

9-07 758 
9.07 863 
9.07 96^ 



9.08 072 
9.08 176 
9.08 279 
9.08 383 
9-o8 486 
9.08 589 

Log. Cos. 



120 
119 
119 
119 
119 
118 
118 
118 
117 
"7 
"6 
116 
116 
116 
"5 
"5 
114 
114 
114 
114 
"3 
"3 
113 

"3 
112 
112 
112 
III 
III 
III 
no 
no 
no 
no 
109 
log 
log 
109 
lo§ 



107 
107 
107 
107 
log 
log 
106 
106 
105 
105 

105 
104 
104 
104 
104 
103 
103 
103 
103 



Log. Tan. 
9.02 162 
9.02 283 
9.02 404 
9.02 525 
9.02 645 



9.02 76§ 

9.02 885 

9.03 004 
9.03 123 
9.03 242 



9.03 361 
903 479 
9-03 597 
9.03714 
9.03 831 



9-03 948 
9.04065 
9.04 18T 
9.04 29^ 
9.04413 



9.04 528 
9.04 643 
9.04758 
9.04 872 
9.04987 



9.05 lOI 
9.05 214 
9.05 32^ 
9.05 440 
9-05 553 



9.05 666 
9.05 778 

9.05 890 

9.06 001 
9.06 1 13 



9.06 224 

9-06335 
9.06445 
9.06 555 
9.06 66 § 



9.06775 
9.06 884 

9.06 994 

9.07 102 
9.07 211 



9.07319 
9.07 428 

9-07 53§ 
9.07 643 
9.07 750 



9.07 85^ 

9.07 964 

9.08 071 
9.08 17? 
9.08 283 



9.08 389 
9.08 494 
9.08 600 
9.08 705 
9.08 810 



9.08 914 

Log. Cot. 



c. d. I Log. Cot. 
0.97838 
0.97 7I6 
0.97 595 
0.97 475 
0.97 354 



121 
121 
120 
120 
I20 
119 
119 
119 
119 

"8 
118 
118 
H7 
117 
117 
"6 
116 
116 
115 
"5 
"5 
114 
114 
114 
114 

"3 
113 

113 
"3 
112 
112 
112 
III 
HI 
III 
III 
no 
no 
no 
109 
109 
109 
io§ 
109 
108 
io§ 
107 
107 
107 

107 

107 
log 
log 
106 
los 
105 
105 
los 
105 
104 

"cTT 



0.97 234 
0.97 115 
0.96995 
0.96876 
0.967 s? 



0.96639 
0.96 521 
0.96 403 
0.96285 
0.96 168 



0.96 051 

0.95935 
0.95 818 
0.95 702 
0.95 587 



0.95471 

0.95 356 
0.95 242 
0.95 127 
0-95013 
0.94899 

0.9478? 
0.94672 

0.94 559 
o- 94 446 

0.94 334 
0.94 222 
0.94 1 10 

o- 93 998 
0.93 887 



0.93776 
0.93 665 
0-93 554 
0.93444 
0.93 334 



0.93225 
0.93 115 
o. 93 006 
0.92 897 
0.92788 



0.92 686 
0.92 572 
0.92 464 
0.92357 
0.92 249 



0.92 142 
0.92035 
0,91 929 
0.91 822 
0.91 716 



Log. Cos. 
9.99761 
9.99760 

9-99 759 
9-99 75? 
9.99756 



9-99 754 
9-99 753 
9.99752 
9.99756 
9-99 749 



9.99748 
9-99 746 
9-99 745 
9-99 744 
9-99742 



9.99741 
9-99 739 
9-99 738 
9-99 737 
9-99 73§ 



9-99 734 
9-99732 
9-99 731 
9.99730 

9-99 728 



9-99727 
9.99725 
9.99724 
9.99723 
9.99721 



9.99720 
9-99 718 
9-99717 
9.99715 

9-99714 
9.99712 
9.99 71 1 
9.99710 

9-99 708 
9.99707 



9.99705 
9.99704 
9-99 702 
9.99701 
9.99699 



9.99698 
9.99696 
9.99695 

9-99693 
9-99692 



0.91 61 1 
0.91 505 
0.91 400 
0.91 295 
0.91 190 



0.91 085 

Log. Tan. 



9.99696 
9.99689 
9.99687 

9.99 686 
9.99684 



9.99683 
9.99681 

9-99679 
9.99678 

999676 



9-99675 

Log. Sill. 



60 

59 
58 
57 

55 
54 
53 
52 
51 
50 
49 
48 
47 

45 
44 
43 

42 

41 
40 

39 
38 
37 
J^ 
35 
34 
33 
32 
31 
30 

29 
28 

27 
26 



24 

23 
22 
21 

"20 

19 
18 

17 
16 



15 
14 
13 
12 
II 

To 

9 

8 

7 
6 



121 


121 


Z20 


119 


118 


12. I 


12. 1 


12.0 


n.Q 


II. 8 


14.2 


14.1 


14.0 


130 


!3-7 


16.2 


16. i 


16.0 


i.S-R 


15-7 


18.2 


18. i 


18.0 


17-8 


17-7 


20.2 


20. 1 


20.0 


19.? 


19-6 


40.5 


40-3 


40.0 


3Q-0 


39-3 


60.7 


bo.s 


60.0 


,S9-,S 


590 


81.0 
101.2 


100.8 


80.0 
100. 


79.3 
99.1 


7Ǥ 
98.3 





11^ 


II 


7 


116 


6 


II. 7 


.1 7 


11.6 


7 


13-7 


13 


6 


13-5 


8 


15-6 


15 


6 


'5-4 


9 


17.6 


'7 


5 


17.4 


10 


19.6 


19 


5 


19.3 


20 


39-1 


39 





38.6 


30 


S8.7 


58 


S 


58.0 


40 


7»-3 


7« 





77-3 


50 


97-9 


97 


5 


90-6 



"5 

"•5 
134 
15-3 
17.2 

19. i 
38.3 
57-S 
76.6 
95-8 



114 114 



15.2 
17.2 
19.1 
38.1 
57-2 
76.3 
95-4 



II. 4 

133 
15.2 
17. 1 

19.0 
38.0 
S7-0 
76.0 
95-0 



"3 

"•3 
13.2 
15.0 
16.9 
18.8 

37-6 
56-5 
75-3 
94.1 



13.0 
14.9 
16.8 
18. § 

37-3 
56.0 

74 •§ 
93-3 





lib 


IIO 


109 


6 


II. 


II. 


10.9 


7 


12 


9 


12.8 


12.7 


8 


14 


7 


14-6 


14-5 


9 


lO 


6 


16. s 


16.3 


10 


18 


4 


18.3 


18. i 


20 


36 


8 


36. g 


36-3 


30 


55 




55*0 


54-5 


40 


73 


6 


73-3 


-2-6 


50 


92 


I 


91-6 


90-8 



12.9 

14.8 

16. 6 
t8.5 
37-0 
55-5 
74.0 
92.5 



108 

10.8 
12.6 
14.4 
16.2 
18.0 
36.0 
54-0 
72.0 
90.0 



10^ 107 106 105 104 



6 


10.7 


10.7 


10.6 


10 


5 


10 


7 


12.5 


12.5 


>2-3 


12 


2 


12 


8 


14-3 


14.2 


14. 1 


14 





13 


9 


lb. I 


16 


15-9 


IS 


7 


15 


10 


17.9 


17-8 


17 6 


17 


S 


17 


20 


35. § 


35-6 


35-3 


35 





34 


30 


53-7 


53-5 


53-0 


52 


s 


52 


40 


71-6 


7'-3 


70-6 


70 





bg 


SO 


89. 6 


89.1 


88.3 


87 


5 


86 





103 


103 


2 


i 


6 


IO-3 


10.3 


0.2 


0.1 


7 


12. 1 


12.0 


0.2 


0.2 


8 


•3-8 


13 


7 


0.2 


0.2 


9 


15-5 


15 


4 


03 


0.2 


10 


17.2 


17 


I 


0-3 


0.2 


20 


34-5 


34 


3 


0.6 


0.5 


30 
40 

50 


51-7 
69.0 
86. S 


51 
68 
8S 


5 
6 
8 


I.O 

1-6 


0.7 
I 
1.2 



P.P. 



83° 



34 



TABLE IV. 



oS 589 
oS 692 
08794 
08897 
oS 999 



9 
10 

II 
12 
13 

u 

15 
16 

17 
18 

19 



09 lOI 
09 202 

09303 
09404 

09503 



09 606 
09706 
09 805 

09906 
0006 



20 

21 



_£4_ 

-5 
26 

27 
28 

_£9_ 

30 

SI 



34 

35 
36 
37 
38 
39 



2 518 
2 612 
2 706 
2 799 
2 892 



298? 
3078 
3 170 
3 263 
3 355 



10 

41 
42 
43 

44 

45 
46 
47 
48 
49 
50 
51 
52 
53 
54 

55 
56 
57 
58 
59 
GO 
I Log. Cos. 



o 105 
o 205 

0303 

o 402 
o 501 



0599 
0697 
0795 

o 892 
o 990 



087 

184 

281 

377 
473 



570 
66| 
761 

856 
952 



2047 
2 141 
2 236 
2330 
2425 



3 447 
3 538 
3630 
3 721 
3 813 
3 903 

3 994 
4085 

4 17% 
4 26g 

4 35? 



102 
102 

I02 
I02 
102 

loi 

lOI 
lOI 
lOI 

100 
100 
100 
100 
99 
99 
99 
98 
99 

98 
98 

98 
97 
97 
97 
97 
96 
97 
96 
96 
96 
95 
96 

95 
95 
95 
94 
94 
94 
94 
93 
94 
93 
93 
93 
93 
92 
92 
92 
92 
92 

91 
92 

91 
9' 
90 

91 
95 
90 
90 

90 



Loi;. Tun. v. d. 

9.08 914 

9090I8 

9.09 123 
9.09 226 

9- 09 330 



9-09 433 
9-09 536 
9.09 639 
9.09 742 
9.09 844 



9.09 947 



048 
o 156 
o 252 

0353 



0454 

0555 
0655 
0756 

o 856 



0956 

o5§ 
155 

254 
353 



452 
550 
649 

747 
845 



943 
2 040 

2 13? 
2 235 
2 331 



2428 
2 525 
2 621 
2717 
2813 



2908 
3004 

3099 
3 194 
3289 



3384 
3 478 
3 572 
3666 
3760 



3854 

3 94? 
4041 

4134 
4227 

4319 

4412 

4504 

4 596 
4688 

4780 
Log. Cot. 



104 
104 
103 
103 
103 
103 
103 
102 

I02 
102 

loi 

I02 

loi 

lOI 
lOI 

lOI 

100 
100 
100 
100 
99 
99 
99 
99 
98 
98 
98 



97 
97 
97 
96 
97 
96 
96 
96 
96 
95 
95 
95 
95 
95 
94 
94 
94 
94 
94 
93 
93 
93 
93 
93 
92 
92 
92 
92 
92 
92 

"cTdT 



Lou'. Cot. 
0.91 085 
o. 90 98 1 
0.90877 
0.90773 
0.90670 



0.90 565 
0.90463 
0.90 366 
0.90 258 
0.90155 



0.90053 
0.89 95T 
0.89 849 
0.89 748 
0.89 647 
0.89 546 
0.89445 
0.89344 
0.89244 
0.89 144 



0.89 044 
0.88 944 
0.88845 
0.88745 
0.88646 



0.88 548 
0.88 449 
0.88 351 
0.88 253 
0.88 155 



0.88057 
0.87 959 
0.87 862 
0.87 765 
0.87 663 



0.87 57T 
0.87475 
0.87 379 
0.87 283 
0.87 187 



0.87 091 

o. 86 996 
0.86 900 
0.86 80 1 
0.86 716 



0.86616 
0.86 521 
0.86427 
0.86333 
0.86 239 



0.86 146 
0.86 052 
0.85959 
0.85 866 
0.85773 



0.85686 
0.85 588 
0.85495 
0.85 403 
0-85311 
0.85 219 

Log. Tan. 

82^ 



oir. Cos 



99(>75 
99673 
99672 
99676 
99 669 
99 66^ 
99665 
99664 
99 662 
99661 

99 659 
99658 
99656 
99654 
99653 



99651 
99650 
99 648 
99646 
99 645 



99643 
99641 
99 640 
99638 
99637 



99635 
99633 
99632 
99 630 
99628 



99627 
99625 
99623 
99 622 
99 620 
99'6T§ 
99617 
99615 
99613 
99 61 1 



99 610 
99608 
99606 
99605 
99603 



99 601 
99 600 
99598 
99 596 
99 594 



99 593 
99591 
99 589 
9958? 
99586 



99584 
99582 
99586 
99 579 
99 577 

9-99 57g 

Log. Sin. 



GO 

59 
58 
57 
56 



55 

54 
53 
52 
51 
50 
49 
48 
47 
46 



45 
44 
43 
42 
41 
40 
39 
38 
37 
36 



35 
34 
33 
32 
31 
30 

29 
28 
27 

-A 
25 
24 



21 

"20 

19 
18 

17 
16 



15 
14 
13 
12 
II 

To 

9 

8 

7 
6 



104 103 



10.4 
12.1 

I3-8 
15 6 
I7§ 
34-6 
52.0 
69.3 
86.6 





lob 


6 


10. 


7 
8 


II. 7 
134 


9 
10 


15. 1 
16.7 


20 


33-5 


30 
40 

5° 


50.2 
67.0 
83.7 



94 

9-4 



10.3 
12.0 

•3-7 
15.4 
17. 1 
34-3 
5'-5 

85-8 



100 

10. o 
II. 6 

'3-3 
15.0 
16.6 

33-3 
50.0 
66.^ 
83.3 



102 

10.2 
II. 9 
13.6 
15-3 
17.0 
340 
510 
68.0 
85.0 



99 

9.9 

"■5 
13-2 

14-8 
16.5 
330 
49-5 
66.0 
82.5 





9l 


97 


96 


6 


9-7 


9-7 


9.6 


7 


11.4 


II. 3 


II. 2 


8 


13.0 


12.9 


12.8 


Q 


14.6 


M-5 


14.4 


10 


16.2 


16. 1 


16.0 


20 


32-5 


32-3 


32.0 


SO 


48.7 


48.5 


48.0 


40 


65.0 


64-6 


64.0 


50 


81.2 


80. § 


80.0 



lOI 

10. 1 
II. 8 
'3-4 
'5-1 
16, § 

33-6 
SO. 5 
67-3 
84.1 



98 

9.8 
II. 4 
13.0 
14.7 
16.3 

32.6 
49.0 

65-3 
81.6 



95 

9-5 
II. I 
12.6 
14.2 
15-8 
31-6 
47-5 
63-3 
79 i 



94 


93 


92 


9-4 


9-3 


9.2 


10.9 


10 


8 


10 


7 


12.5 


12 


4 


12 


2 


14. 1 


13 


9 


13 


8 


15-6 


'5 


5 


15 


3 


31-3 
47.0 
62.^ 
78.3 


11 
46 
62 



5 



30 
46 
61 


6 


3 


77 


5 


76 


6 





91 


91 


90 


2 


6 


9.1 


9.1 


9.0 


0.2 1 


7 


10.7 


10.6 


10. 5 





2 


8 


12.2 


12. 1 


12.0 





2 


9 


13-7 


'3-6 


135 





3 


10 


15.2 


15-1 


15.0 





3 


20 


30-5 


30-3 


30.0 





6 


so 


45-7 


45-5 


45-0 


I 





40 


61.0 


60.6 


60.0 


I 


3 


50 


76.2 


75-8 


75° 


I 


6 



P. p. 



35 



8^ 



TABLE IV. 



10 

II 

12 

13 

H 

15 
i6 

17 
i8 

19 



20 

21 

22 

23 
24 



25 
26 

27 
28 
29 



30 

31 
32 
33 
34 



35 
36 
37 
38 
39 



40 

41 
42 

43 
44 



45 
46 

47 
48 

49 

50 

51 
52 
53 
54 

55 
56 
57 
58 
59 
«0 



Log. Sin. 

9-14355 
9.14445 

9-14 535 
9.14624 

9-14713 



9.14802 
9. 14 891 
9.14980 
9.15068 
9-15 157 



9.15245 

9-15333 
9.15421 

9-15 508 
9- 1 5 595 



15683 
15770 
15857 
15943 
16 030 



9.16 116 
9.16 202 
9.16 283 
9.16374 
9. 1 6 460 

9-16545 
9.16 630 
9. 16 716 
9.16 801 
9.16885 



9.16 970 
9.17054 

9.17 139 
9.17 223 
9.17307 



9.17 391 

9.17474 
9-17558 
9-17641 
9.17724 



9.17 807 

9. 1 7 890 
9.17972 
9.18055 

9.18 137 



9.18 219 
9.18 301 

9.18383 
9.18465 

9.18546 



9.18 628 
9. 1 8 709 
9.18 790 
9.18871 
9.18952 



19032 
19113 

19 193 
19273 

19353 



9-19433 
Log. Cos. 



90 

89 



89 
89 

88 



^7 
8f 
87 
87 
86 
86 



85 
85 

85 
85 

85 
84 



84 



83 
83 
83 
83 
83 
83 
82 
82 
82 
82 
82 
82 
81 
81 
81 
81 
81 
86 
81 
80 
86 
86 
80 
80 

79 



Log. Tan. 
9.14786 
9.14872 
9.14963 
9.15054 

9- '5 h5 



9-15236 
9.15327 

9-1541? 
9.15 sof 
9. 1 5 598 



9.1568^ 

9-1577? 
9-15867 

9-15 956 
9. 16 045 



9.16 134 
9. 16 223 
9. 16 312 
9.16 401 
9. 16 489 



9.1657? 
9.16665 
9.16753 
9.16 841 
9.16928 



9-17015 
9.17 103 
9.17 190 
9.17276 
9-17 363 



9.17450 
9.17536 
9. 17 622 

9- 1 7 708 
9.17794 



9. 1 7 880 
9.17965 

9. 1 8 05 1 
9.18 136 
9.18 221 



9. 1 8 306 
9.18 396 
9.18475 
9.18559 
9. 1 8 644 



9.18728 
9.18812 
9.18896 
9.18979 
9.19063 



9.19 146 
9.19 229 
9-19312 
9-19395 
9.19478 



9.19 566 
9.19643 
9.19725 
9.1980^ 
9.19 889 

9- 19 971 
Log. Cot^ 



c. d. 

91 
91 
91 
91 
91 
90 
96 

90 
96 

89 

90 

89 
89 
89 
89 

89 
89 
88 



8? 
88 
87 
87 
8? 
87 
86 
87 

86 
86 



85 
85 
85 
85 
85 
84 



84 
84 
84 

83 
83 
83 
83 
83 
83 
82 

82 
82 
82 
82 
82 
82 

7737 



Log. Cot. 
0.85 219 
0.85 128 
0.85 037 
0.84945 
0.84 854 



0.84763 
0.84673 
0.84 582 
0.84492 
0.84402 



0.84 312 
0.84 222 
0.84133 

o. 84 043 

0.83954 
0.83865 
0.83776 
0.8368? 
0.83 599 
0.83 511 



0.83 422 
0.83334 
0.83 247 
0.83 159 
0.83 07T 



0.82 984 
0.82 897 
0.82 810 
0.82 723 
0.82636 



0.82 550 
0.82 464 
0.82 37? 
0.82 291 
0.82 206 



62 120 

82 034 

81 949 

81 864 

81 779 



81 694 
81 609 
81 525 
81 446 
81356 



81 272 
81 188 
81 104 
81 026 
80937 



O, 
O, 
O, 

o, 
o, 
o, 
o 
o 
o 
o. 
o. 
o, 
o, 
o, 
o. 
o, 
o. 
o. 
o. 
o 
o, 
o, 
o, 
o 
o 
Log. Tan. 

81 



80854 
80 776 
8068? 
80 604 

80 !;22 



80439 
80357 
80 274 
80 192 
80 1 16 

.80023 



Log. Cos. 

9-99 575 
9-99 573 
9.99 571 

9-99 570 
9.99 568 



9-99 566 
9-99 564 
9-99563 
9.99 561 

9-99 559 



9-99 55? 
9-99 555 
9-99 553 
9-99 552 
9.99 550 



9-99 548 
9-99 546 
9-99 544 
9.99 542 
9.99541 



9-99 539 
9-99 537 
9-99 535 
9-99 533 
9-99 531 



9.99529 
9.99528 
9.99526 
9.99524 
9-99 522 
9.99 520 
9-99 518 
9-99 516 
9-99514 
9.99512 



9.99 511 

9-99 509 
9.99507 

9-99 505 
9-99 503 



9-99 501 
9.99499 
9.9949? 
9.99495 
9-99 493 



9-99491 
9.99489 
9.9948? 

9-99485 
9.99484 



9.99482 
9.99480 
9.99478 
9.99476 
9-99 474 



9.99472 
9.99470 
9.99468 
9.99466 
9-99464 
9-99462 

Log. !Sin. 



GO 

59 
58 
57 

55 
54 
53 
52 
51 
50 
49 
48 

47 
46 



45 

44 
43 
42 

41 
40 

39 
38 

37 
36 



35 
34 
33 
32 
31 
30 

29 
28 
27 
26 



25 
24 
23 
22 
21 

lo 

19 
18 

17 
16 



15 
14 
13 
12 
II 

lo 

9 
8 

7 
6 



P. P. 





9i 


91 


90 


6 


9-1 


9-1 


9-0 


7 


10.7 


10.6 


10.5 


8 


12.2 


12.T 


12.0 


9 


13-7 


13-6 


13-5 


10 


15.2 


15.1 


15.0 


20 


30.5 


30.3 


30.0 


30 


45-7 


4S-5 


4S-0 


40 


61.0 


60.6 


60.0 


50 


76.2 


75-8 


75.0 





88 


88 


87 


6 


8.8 


8.8 


8.7 


7 


10. s 


10.2 


10. T 


8 


11.8 


II-? 


II. 6 


9 


13-3 


13.2 


13.0 


10 


14.7 


14-6 


14.5 


20 


29.5 


29-3 


29.0 


30 


44-2 


44-0 


43-5 


40 


59.0 


58.6 


58.0 


50 


73-7 


73-3 


72.5 



89 

8.9 

10.4 
II. 8 
13-3 
14-8 
29-6 
44-5 
59-3 
74-1 

86 

8.6 
10.6 
II. 4 
12. 



8S 85 

8.5 
lo.o 
II. 4 

12.8 
14.2 
28.5 
42.? 
57-0 
71.2 



82 

8.2 
9.6 

II. o 

12,4 
I3-? 
27-5 
41.2 
55.0 
68.? 



82 

8.2 

9-5 
10.9 
12.3 
13-6 

27-3 
41.0 

54-6 
68.3 



84 

8.4 
9.8 
II. 2 
12.6 
14.0 
28.0 
42.0 
56.0 
70.0 

81 

8.1 

9.4 

10.8 

12. T 

13-5 
27.0 
40.5 
54.0 



83 



80 

8.0 
9-3| 

10.6! 

12.0 

13-31 
26.6 1 
40.0 

53-3 i 
67.5 166.6 



6 

7 
8 

9 
10 

20 

30 
40 

50 



79 

7-9 
9-3 
10.6 
II. 9 
13.2 
26.5 

39-? 
53-0 
66.2 



2 

0.2 
0.2 
0.2 
0.3 
0.3 
0.6 
i.o 

1-3 
1-6 



P.P. 



I 
o. T 
0.2 
0.2 
0.2 
0.2 

0.5 
o.? 
1.0 
1.2 



36 



TABLE IV. 



9 
10 

II 

12 

13 
U 

15 
i6 

17 
i8 

19 



20 

21 

22 
23 
24 



-^5 
26 

27 
28 
29 



30 

31 
32 
33 
34 



35 
36 
37 
38 
39 



40 

41 
42 

43 
44 

45 
46 
47 
48 

49 



50 

51 
52 
53 
54 

55 
56 
57 
58 
59 
60 



Loy. Sill. 



'9 433 
i95'3 
19592 
19672 
19751 



19 830 
19909 
19988 
20065 
20145 



20 223 
20 301 
20379 
2045? 
20535 



20613 
20690 
20768 

20845 
20 922 



20 999 
076 
152 
229 
305 



382 
458 
534 
609 
68? 



761 

836 
911 
987 
22 062 



22 136 
22 21T 
22 286 
22 366 
22435 



22 509 
22 583 
22 65^ 
22 731 
22 805 



22878 

22 952 

23 025 
23098 
23^71 
23244 
23317 
23390 
23 462 
23535 



23 60^ 
23679 

23751 
23823 

23895 

9-23967 
Log. Cos. 



80 
79 
79 
79 
79 
79 
79 
78 
78 
78 
78 
78 
78 
78 
11 
11 
11 
11 
11 
11 
11 
76 
76 
76 

76 
76 
76 

1% 
76 

7S 
7§ 
75 
75 
75 
74 
75 
74 
74 
74 
74 
74 
74 
73 
74 
73 
73 
73 
73 
73 
73 
72 

73 
72 

72 
72 
72 
72 
72 
72 

71 



,i>jf. Inn. 

19971 
20053 
20 134 
20 216 
20 297 
20 378^ 
20459 
20540 
20 626 
20 701 



20 78T 
20862 
20942 
022 
102 



181 
261 

340 
420 

499 



578 
657 

735 
814 



971 
22 049 
22 127 
22 205 



22 360 
22438 

22.515 
22593 
22 670 



22747 
22 824 
22 906 
2297? 
23054 



23 130 
23206 

23 282 

23 358 
23434 
23 516 
23586 
23 661 

23737 
23 812 



23887 

23 962 
24037 

24 112 
24186 



24 261 

24335 
24409 
24484 
24558 
24632 

Log. Cot. 



c. (1. 

81 
81 

8r 
81 
81 
81 
81 

86 
81 
80 
86 
80 
80 
80 

79 
79 
79 
79 
79 
79 
79 
78 
78 
78 
78 
78 
78 
78 
78 

11 
11 
11 
11 
11 
11 
11 
76 
11 
76 
76 

76 
76 
76 
76 
76 
75 
75 
75 
75 
75 
75 
75 
75 
74 
74 
74 
74 
74 
74 
74 



9' 



80 02y 

79 947 
7986? 

79784 
79703 



79622 

79541 
79460 

79 379 
79298 



79218 
79138 
79058 
78978 
78898 



78818 

78739 
78659 
78 5S0 
78 501 



78422 

78 343 
78 264 
78 186 
78 10^ 



78 029 
11 951 
11 873 

n 795 
11 717 



77 639 
11 562 
77484 
77407 

11 330 



11 253 

71 176 
77099 
jj 022 
76946 



76 870 
76793 

7671? 
76 641 
76565 



76489 
76414 

76338 
76 263 
76 j88 



76 113 
76038 

75963 
75888 

75813 



75 739 
75664 

75590 
75516 
75442 
75368 

Log. Tan. 

80= 



99 4'J2 
99 460 

99 458 
99456 

99 454 



99452 
99450 

99 448 
99446 
99 444 



99442 
99440 
99^43? 
99 435 
99 433 



99431 
99429 

99427 

99425 
99 423 



99421 
99419 
99417 
99415 
9 9413 
99 41 1 
99408 
99406 
99404 
99 402 



99400 

99398 
99396 

99 394 
99392 



99389 
99387 
99385 
99383 
99381 



99 379 
99 377 
99 374 
99372 
9 9370 
99 368 
99 366 

99364 
99361 

99 359 



99 357 
99 355 
99 353 
99350 
99 348 



99346 
99 344 
99342 
99 339 
99 33^ 
999 335 

Log. Sin. 



(>0 

59 
58 
57 
Ji. 
55 
54 
53 
52 
51 
60 
49 
48 
47 

45 
44 
43 
42 
41 
40 
39 
38 
37 

35 
34 
33 
32 
31 
30 
29 
28 
27 
26 



25 

24 
23 
22 
21 

"20 

19 
18 

17 
16 



15 
14 
13 
12 
II 

To 

9 

8 

7 
6 



r. r. 





8i 


81 


80 


79 


6 


8.1 


8.1 


8.0 


7- 


7 
8 


9-5 
10.8 


9.4 
10.8 


9-3 
10 6 


9- 
10. 


9 


12.2 


1 2. 1 


12,0 


1 1. 


10 
20 


13.6 

27. T 


135 
27.0 


'3-3 
26.6 


13- 
26. 


30 
40 
50 


40.? 

54-3 
67.9 


40.5 
54.0 

67.5 


40.0 

53-3 
66.6 


39- 
52. 
65- 





78 


78 


77 


6 


7-8 


7.8 


1-1 


7 
8 


9.1 
10.4 


91 
10.4 


9.0 
10.2 


9 


II. 8 


II. 7 


II. § 


10 
20 


131 
26. T 


13.0 
26.0 


12.8 
25-6 


30 


39-2 


390 


38.5 


40 
50 


52.3 
65.4 


52.0 
65.0 


51-3 
64. T 



76 

7-6 
8.9 
10.2 
II. 5 
12.^ 
25.5 
38.2 
51.0 
63-? 



76 

7.61 

8.8 
10. T 
II. 4 
12.6 

25-3 
38.0 

50.6 



75 

7-5 
8.^ 
lo.o 
II. 2 
12.5 
25.0 

37-5 
50.0 



63-3,62.5 



74 
7-4 
8.6 
9-8 
II. I 
12.3 

24-6 
37-0 
49-3 
61.6 



6 

7 
8 

9 
10 
20 
30 
40 
50 



73 

7-3 
8.6 
9.8 

II. o 

12.2 

24-5 
36.7 
49.0 
61.2 



73 

7-3 
" 5 
7 
9 
I 





71 


71 


2 


6 


7-1 


7-1 


0.2 


7 


8.3 


8-3 


0-3 


8 


9-5 


9.4 


0-3 


9 


10.7 


10.6 


0.4 


10 


II. 9 


II. 8 


0.4 


20 


23-8 


23-6 


0.8 


30 


35-7 


35-5 


1.2 


40 


47-6 


47-3 


1-6 


50 


59-6 


59-1 


2.1 



72 

7.2 
8.4 
9.6 

10.8 

12.0 
24.0 
36.0 

48.0 

60.0 



2 

0.2 
0.2 
0.2 
03 
0.3 
0.6 
I.O 

1-3 
1-6 



37 













10 


3 














TABLE IV 


• 


/ 


Log. Sill. 


(1. 


Log. Tan. 


c. d. 


Log. Cot. 


Log. Cos. 




p. p. 






I 

2 

3 

4 


9.23967 

9-24 038 
9.24 no 
9.24 181 
9.24252 


71 
7t 
71 
71 
71 
71 
71 
71 
70 

70 
70 
70 

70 
70 
69 
70 
69 
70 
69 
69 
69 
69 
69 
69 

68 
69 
68 
68 
68 

68 
68 
68 
68 
6? 
6? 
68 
67 
6? 
67~ 

67 
67 
67 
66 
67 

66 
66 
66 
66 

66 
66 
66 

65 
66 

65 

65 

65 

^} 
65 

65 

65 


9.24632 
9.24705 
9.24779 
9.24853 
9.24926 


73 
74 
73 
73 
73 
73 
1^ 
72> 
72. 

73 
72 

72 
72 
72 

72 
72 

72 
72 
71 
72 
7f 
71 
71 
71 
71 
71 
70 

71 
70 
70 
70 

70 
70 
70 
70 
70 

69 
70 

69 

69 
69 
69 

69 
69 

69 
69 
68 
69 
68 

68 
68 

68 
68 

68 
68 

6? 
68 
6? 
6? 
6? 


0.75368 
0.75294 
0.75 220 
0.75 147 
0.75073 


9-99 335 
9-99 333 
9-99330 
9-99 328 
9-99326 


00 

59 
58 
57 
56 


6 

7 
8 

9 
10 
20 
30 
40 


74 
7-4 
8.6 
9-8 
II. I 
12.3 

24-6 
37-0 
49-3 


73 

7-3 

8.6 

9.8 

II. I 

12.2 I 
24.5 2 

36.? 2 
49.0 ^ 


73 

7-3 
8.5 

9-? 
0.9 
2.1 

4-3 

6.5 

.8.6 

0-8 

71 

7-1 

8.3 

9-4 

10.6 

II. 8 

23-6 

35-5 

47.3 

59-1 

69 

6.9 

8.6 

9.2 

10.3 

II-5 
23.0 

i34-5 
46.0 

;57-5 
67 

6.7 

7.S 

8.9 

10.6 

II. T 

22. 3j 

33-5 

44-6 

55-8 

65 

6.5 

7.6 

8.6 

9-?i 

10.8 ! 

21.61 

32-5 

43-3 
54-1 




5 
6 

7 
8 

9 


9-24323 
9-24 394^ 
9.24465 

9-24 536 
9.24607 


9.25 000 
9.25073 
9.25 146 
9.25219 
9.25292 


0. 7 5 000 
0.74927 
0.74854 
0.74781 
0.74708 


9-99324 
9.99321 

9-99319 
9-99317 
9-99315 


55 
54 
53 
52 
51 
50 

49 
48 

47 
46 




10 

II 

12 

13 

14 


9-2467? 
9.24 748 
9.24818 
9.24888 
9-24 958 


9-25 365 
9-2543? 
9.25510 
9.25 582 
9.25654 
9.25727 

9-25799 
9.25 871 

9.25 943 

9.26 014 


0.74635 
0.74562 
0.74490 
0.7441? 
o- 74 345 
0.74 273 
0.74 201 
0.74129 
0.74057 
0.73985 


9.99312 
9.99316 
9.99308 
9.99306 
9-99303 


6 

7 
8 

9 
10 

20 
30 
40 
50 

6 

7 
8 

9 

10 
20 
30 

40 

50 

6 

7 
8 

9 
10 
20 

30 
40 

50 

6 

7 
8 

9 
10 

20 
30 
40 
50 


5o|bi 
72 
7.2 
8.4 
9-6 


•6|b 
72 
7.2 
8.4 
9.6 


1.2 1 e 
71 

7-1 

8.3 

9-1 

10.7 

II. 9 

23-8 

35-? 

47-6 

59-6 

69 

6.9 

8.1 

9.2 

10.4 

II. 6 

23.1 

34.? 

46.3 

57-9 

6f 

6.? 

7-9 
9.0 

10. 1 

11. 2 
22.5 

33-? 
45.0 
56.2 

6S 

6.5 
7.6 
8.? 
9-8 
10.9 

21.8 
32.? 
43-6 
54-6 

2 
0.2 
0.2 
0.2 




15 
i6 

17 
i8 

19 


9.25 028 
9.25 098 
9.25 16? 
9-25237 
925306 


9.99301 

9-99299 
9.99296 
9.99294 
9.99292 


45 
44 
43 
42 

41 


10.9 
12. 1 

24.1 
36.2 

48.3 
60.4 

70 

7.0 
8.2 

9-4 
10.6 
II.? 

23-5 
35-2 
47.0 
58.? 

68 

6.8 

8.0 

9.1 

10.3 

II. 4 

22.8 

34-2 

45-6 

57-1 

68 

6.6 

7.? 

8.8 

lO.O 

11. 1 

22.1 
33-2 

44-3 
55-4 

6 

7 
8 


10.8 
12.0 

24.0 

36.0 

48.0 

60.0 

70 

7.0 

8.1 

9-3 
10.5 

II. 6 

23-3 

35-0 

46.6 

58.3 

68 

6.8 

7-9 

9.6 

10.2 

II-3 
22.6 
34.0 
45-3 
56^6 
66 
6.6 

7-7 
8.8 

9-9 
II. 
22.0 
33-0 
44.0 
55.0 
2 

0.2 

0-3 
0.3 
0.4 
0.4 

0.8 
1.2 

1-6 
2.1 




20 

21 
22 
23 
24 


9.25376 
9.25445 
9.25514 

9-25 583 
925652 


9.26 085 
9.26 158 
9.26 229 
9. 26 300 
9,26371 


0-73913 
0.73842 
0.73771 
0.73699 
0.73628 


9.99290 
9.99287 
9.99285 
9.99283 
9.99 280 


40 

39 
38 
37 
36 

35 
34 
33 
32 
31 




25 
26 

27 
28 
29 


9.25721 
9.25 790 

9-25858 
9.25927 
9.25995 


9.26443 
9.26514 
9.26584 
9.26655 
9.26 726 

9-26 796 
9.26867 
9-2693? 
9.27007 
9.27078 


0.73557 
0.73 486 

0.73415 
0.73344; 
0.73274 


9.99278 
9.99276 
9.99273 
9.99271 
9.99269 




30 

31 

32 

33 
34 


9.26063 
9.26 131 
9.26 199 
9.26 26f 

9-26335 


0.73 203 

0.73 133 
0.73 062 
0.72 992 
0.72 922 


9.99266 
9.99264 
9.99 262 
9.99259 
9.99257 


30 

29 
28 
27 
26 




35 
36 
37 
38 
39 


9. 26 402 
9.26470 

9-26537 

9.26605 
9.26672 


9.27 148 
9.27 218 
9.27 287 

9-27 35? 
9.27427 


0.72 852 
0.72 782 
0.72 712 
0.72 642 
0.72 573 


9.99255 
9.99252 
9.99250 
9-99 248 
9.99245 


25 
24 
23 
22 
21 




40 

41 

42 
43 
44 


9.26739 

9. 26 805 

9.26873 

9 26 940 

9.27 007 


9-27 496 
9.27 566 
9-27635 
9.27704 
9-27 773 


0.72 503 
0.72434 
0.72 365 
0.72295 

0.72 226 


999243 
9.99246 
9.99238 
9.99236 
9-99233 


20 

19 
18 

17 
16 




45 
46 

47 
48 

49 


9.27073 
9.27 140 
9-27 206 
9.27272 
9-27 339 1 


9.27842 
9.27911 

9.27 980 

9.28 049 
9.28 II? 


0.72 15? 
0.72 083 
0.72 020 
0.71 951 
0.71 882 


9.99231 
9-99 228 
9-99 226 
9-99224 
9.99 221 


15 
14 
13 
12 
II 




50 

51 
52 
53 

1 54 


9.27405 
9.27471 

9-27 536 
9.27 602 
9.27668 


9.28 186 
9.28254 
9.28 322 
9-28390 
9.28459 


0.71 814 
0.71 746 
0.71 67? 
0.71 609 
0.71 541 


9-99219 
9-99 216 
9.99214 
9.99212 
9.99209 


10 

9 
8 

7 
6 




55 
56 
57 
58 
59 


9-27 733 
9.27799 
9.27 86$ 
9.27929 
9.27995 


9.28527 
9.28 594 
9.28662 
9.28730 
9.2879? 


0.71 473 
0.71 405 

0.71 33? 
0.71 270 
0.71 202 


9.99207 
9.99204 
9.99 202 
9-99 199 
9-99 197 


5 
4 
3 

2 

I 


9 
10 
20 
30 
40 
50 


0.3 
0-3 
0.6 

I.O 

1-3 




60 


9.28 060 


9.28865 


0.71 135 


9.99 194 







Log. Cos. 1 


d. 


Log. Cot. 


^^d. Log. Tan. 1 Log. Sin. | 


' p. P. II 





79' 



38 



TABLE IV. 



1 1 



I,(Hf. Tim. c. (I. l>oif. Cot. 



liOif. Cos. 



P. I'. 



10 

II 

12 

13 

U 



15 
i6 

17 
i8 

19 



20 

21 
22 

23 

24 



26 

27 
28 

29 

30 

31 

32 
33 
34 



35 
36 
37 
38 
39 



40 

41 

42 

43 
44 



45 
46 

47 
48 

49 



50 

51 
52 
53 

54 

55 
56 
57 
58 
59 
60 



28 060 
28 125 
28 189 
28254 
28319, 
283S3 
28448 
28 512 

28576 
28641 



28705 
28 769 
28832 
28896 
28 960 



29023 
29087 
29 150 
29 213 
29277 



29 340 
29403 
29466 

29528 
29591 



29654 

29716 
29779 
29841 
29903 



29965 
30027 
30089 
30151 
30213 



30275 
30336 
30398 
30459 
30526 



30582 
30643 
30704 
30765 
30826 



30886 
3094? 



008 



129 



189 
249 
309 
370 
429 



489 

549 
609 
669 
728 
788 

Log. Cos. 



65 
64 
65 
64 

64 
64 
64 
64 
64 
64 
64 
63 
64 
63 
63 
63 
63 
63 
63 
63 
63 
63 
62 

63 
62 
62 
62 
62 
62 
62 
62 
62 
62 
61 
62 

6 

6 

6 

6 

6 

6 

6 

6 

6 

60 

61 

60 

60 

65 

60 

60 

60 

60 

59 

60 

60 

59 
60 

59 

59 



9.28 865 



2893 
29000 
29 067 
29 134 



29 201 
29 268 

29335 
29 40 1 

29468 



29535 
29 601 
29667 

29734 
29 800 

29866 

29 932 
29998 
30064 

30 129 



30195 
30 260 
30 326 
30391 
30456 



30 522 

30587 
30652 
30717 
30781 



30846 

30 911 

30975 
31040 

31 104 



168 
232 
297 
361 

424 



552 
616 
679 

743 



806 



933 
996 
32059 



-72 122 

32 185 
32 248 
32310 
32 373 




Log. Cot. 



6? 
67 
67 
67 
6? 
66 
67 

66 
67 

6S 
68 
66 

6§ 
66 

66 
66 
66 
66 
65 
65 
65 
65 
65 
65 
65 
65 
65 
65 
64 

65 
64 
64 
64 
64 
64 
64 
64 
64 
63 
64 
64 
63 
63 
63 
63 
63 
63 
63 
63 
63 
63 
63 
62 

63 
62 
62 
62 
62 
62 
62 

TTdT 



0.71 135 
0.71 067 
0.71 000 
0.70933 
0.70 866 



9-99 '94 
9.99 192 
9.99 189 
9.99 187 
9.99 185 



0.70798 
0.70732 
0.70 665 
0.70 598 
0-70 53' 
0.70465 

0.70398 
0.70 332 
0.70 266 
0.70 200 
0.70 134 
0.70 068 
o. 70 002 
0.69 936 
0.69 876 



9.99 182 
9.99 180 
9.99 177 

9-99175 
9.99 172 



9.99 170 
9.99 16^ 
9.99165 
9.99 162 
9.99 160 



9.99 157 
9-99155 
9-99 152 
9.99 150 
9.99 14^ 



0.69 805 
0.69739 
0.69 674 
0.69 608 
0.69 543 



9-99 145 
9.99 142 

9-99139 
9-99137 
9-99134 



0.69478 
0.69413 
0.69 348 
0.69 283 
0.69 218 
0.69 153 
0.69 089 
0.69 024 
0.68 960 
0.68 896 



9.99 132 
9.99129 
9.99127 
9.99124 
9.99 122 



9.99119 
9.99 116 
9-99 I '4 
9.99 III 
9-99 109 



0.68 831 
0.68 76^ 
0.68 703 
0.68 639 
0.68 575 



0.68 51 T 
0.68 44^ 
0.68 384 
0.68 326 
0.68 257 



0.68 193 
0.68 136 
0.68 067 
0.68 004 
0.67 941 



0.67 878 
0.67 815 
0.67 752 
0.67 689 
0.67 626 
0.67 564 
0.67 501 
0.67 439 
0.67 377 
0-67 3'4 
0.67 252 
Log. Tail. 

78^ 



9.99 106 
9.99 104 

9.99 lOI 

9.99098 
9.99096 



9-99093 
9.99091 

9.99088 

9.99085 
9.99083 



9.99 086 

9-9907? 
9.99075 
9.99072 
9.99069 



9.99067 
9.99064 

9.99062 

9.99059 
9-99056 



9.99054 
9.99051 

9.99048 
9-99046 
9-99043 

9-99040 

Log. Sin. 



59 
58 
57 
Ji 
55 
54 
53 
52 
51 
50 

49 
48 

47 
46 



45 
44 
43 
42 
41 
40 
39 
38 
37 
_36 

35 
34 
33 
32 
3' 
30 
29 
28 

27 
26 



-3 
24 
23 



21 
"20 

19 
18 

17 



16 



15 
14 
13 
12 
II 

To 

9 

8 

7 
6 

5 
4 
3 
2 
I 

~0 



6 

7 
8 

9 
10 
20 

30 

40 

50 

66 

6.( 

7-; 

8.i 
io.< 
II. 

22.: 
33-' 
44-: 
55-' 
64 
6.4 
7 



6-7 

6.? 

7-9 

9.0 

10. T 

II. 2 

22.5 

33-? 

45.0 

56.2 

66 



67 

6.7 
7.8 
8.9 
lo.o 
II. I 
22. 3 
33-5 
44-6 
55-8 
6S 



6 

7 
8 


6.6 
7.7 
8.8 


6.6 

7-7 
8.8 


6.5 

7-6 
8.7 


6. 

7- 
8. 


9 
10 


lO.O 

II. I 


9.9 
II. 


9-8 
10.9 


9- 
10. 


20 


22.1 


22.0 


21-8 


21. 


30 
40 
50 


33-2 
44-3 
55-4 


33-0 
44-0 
55-0 


32.7 
43-6 
54.6 


32. 
43- 
54- 



8 

9 
10 
21 
32 
43 
53 

62 



64 

6.4 
7 " 



9 
10 

21 

32 
42 

53 
62 



63 

6.3 

4 
4 
5 
6 
I 



6.2 


6.2 


6.1 


6. 


7-3 
8. .3 


7.2 
8.2 


7.2 
8.2 


7- 
8. 


9-4 
10.4 


9.3 
10.3 


9.2 
10.2 


9- 
10. 


20.8 
31.2 

41.6 
52.1 


20.6 
31.0 

41-3 
5'-6 


20.5 

30-7 
41.0 
51.2 


20. 

30. 
40. 
50. 



66 



6 


6.0 


6.0 


5- 


7 
8 


7.0 
8.6 


7.0 
8.0 


6. 

7- 


9 
10 


9-1 
10. 1 


9.0 

lO.O 


8. 
9- 


20 


20.1 


20.0 


19. 


30 
40 
50 


30.2 

40.3 
50.4 


30.0 
40.0 
50.0 


29. 

39- 
49. 



9 

10, 
21 

31 
42 
52 
61 

I 

60 

6. 

7. 
8. 

9- 
o. 
o. 
0. 
o. 

0. 
2 



65 ' 

5 
6 

6 



6 

5 
3 
I 

63 



9 

10, 
21 

31 

42 

52 
61 
I 



59 

•9 
.9 
•9 
•9 
-9 
-8 

•7 

-6 
.6 



6 


0.3 


0.2 


7 


0.3 


0.3 


8 


0.4 


0.3 


9 


0.4 


0.4 


10 


0.5 


0.4 


20 


I.O 


0.8 


30 


1-5 


1.2 


40 


2.0 


1-6 


50 


2.5 


2.1 



P. p. 



0.2 
0.2 
0.2 

0.3 
0.3 
0.6 

1.0 
1-3 
1.6 



39 



12' 



TABLE IV. 



Lost. sin. 



15 
16 

17 
18 

19 



20 

21 
22 
23 

24 

25 
26 

27 
28 

29 

30 

31 
32 
33 
34 



35 
36 

37 
38 
39 



40 

41 
42 
43 
44 



45 
46 

47 
48 

49 



50 

51 

52 
53 
54 

55 
56 
57 
58 
59 
60 



10 

II 
12 

13 
14 



31 788 
31 847 
31 906 
31 966 
32025 



32084 

32 143 
32202 
32 266 
32319 



32378 
32436 
32495 
32 553 
32 611 



32670 
32728 
32786 

32844 
32902 



32960 
3301? 
33075 
33 133 
33 190 



33248 
33305 
33362 

33419 

33 476 



33 533 
33590 
33647 
33704 
33761 



3381? 
33874 
33930 
33987 
34043 



34099 
34156 
34 212 
34268 
34324 



34 379 
34 435 
34491 
34 547 
34602 



34658 
34713 
34768 
34824 

34879 



34 934 
34989 
35044 
35099 

35 154 
9-35209 

Log. Cos. 



59 
59 
59 
59 
59 
59 
59 
58 
59 
58 
58 
58 
58 
58 

58 
58 
58 
58 
58 
58 
57 
58 
57 
Si 
Si 
57 
Si 
57 
57 
57 
57 
57 
57 
56 
56 
56 
56 
56 
56 
56 
56 
56 
56 
56 
55 
56 
55 

56 

55 
55 
55 
55 
55 
55 
55 
55 
55 
54 
55 
55 



Lost. Tan. 



747 
809 
871 
933 
995 



057 
118 
186 
242 
303 



364 
426 

487 
548 
609 



670 

731 
792 
852 
913 



974 
034 
095 
155 
215 



275 

396 
456 
515 



575 
635 
695 
754 
814 



873 
933 
992 
051 
no 



169 

228 

28^ 
346 
405 



464 

58? 

640 



756 
815 
873 
931 
989 



04^ 
105 
163 
221 
278 



36336 

Log^Cot^ 



Log. Cot. 

0.67 252 
0.67 196 
0.67 128 
o. 67 065 
0.67 004 
0.66 943 
0.66 881 
0.66 819 
0.66 758 
0.66 696 
0.66 635 
0.66 574 
0.66 513 
0.66 452 
0.66 396 



0.66 330 
0.66 269 
0.66 208 
0.66 147 
0.66 085 



0.66 026 
0.65 965 
0.65 905 
0.65 845 
0.65 784 



0.65 724 
0.65 664 
0.65 604 
0.65 544 
0.65 484 



62 
62 
62 
62 
61 
61 
62 
61 
61 
61 
6i 
61 
6t 
61 
66 
61 
61 
60 
61 
60 
66 
66 
60 
60 
60 
66 
60 
60 
59 
60 
60 
59 
59 
59 
59 
59 
59 
59 
59 
59 
59 
59 
59 
59 
58 
58 
59 
58 
58 

58 
58 
58 
58 
58 
58 
58 
Si 
58 
Si 
58 

c. (I. I Log. Tan. 



0.65 424 
0.65 364 
0.65 305 
0.65 24§ 

0.65 186 



0.65 125 
0.65 067 
0.65 008 

0.64948 

0.64 889 



0.64 836 
0.64 771 
0.64 712 
0.64 653 
0.64 594 



0.64 536 
0.64477 
0.64418 
o. 64 360 
0.64 302 



0.64 243 
0.64 185 
0.64 127 
0.64068 
0.64016 



0.63952 
0.63 894 
0.63 837 
0.63 779 
0.63 721 
0.63663 



Log. Cos. 

99 046 



99027 

99024 

99021 

99019 

99016 

9.99013 

9.99016 

9. 99 008 

9.99005 

9.99002 



99038 

99035 
99032 
99029 



98999 
98997 

98 994 
98991 



98986 
98983 
98986 
9897? 
98975 



98972 
98 969 
98965 
98963 
98 961 

98958 
98955 
98952 
98949 
98947 



98944 
98941 

98938 
98935 
98933 



98930 

98927 
98924 
98 921 
98918 



98915 
98913 
98 910 
98907 
98 904 



98 901 
98898 
98895 
98892 
98890 



98887 
98884 
98881 
98878 
98875 
9.98 872 
Log. Sin. 



60 

59 
58 

57 
56 



55 
54 
53 
52 
51 
50 
49 
48 
47 
_46_ 

45 
44 
43 
42 
41 
40 
39 
3^ 
37 
36 



35 
34 
33 
32 
31 
30 

29 
28 
27 
26 

25 
24 
23 
22 
21 

"20 

19 
18 

17 
16 



15 
14 
13 
12 
II 

To 

9 

8 

7 
6 





62 


61 


6] 


6 


6.2 


6.T 


6. 


7 
8 


7-2 

8.2 


7.2 
8.2 


7- 
8. 


9 
10 


9-3 
10.3 


9.2 
10.2 


9- 
10. 


20 


20.6 


20.5 


20. 


30 
40 
50 


31.0 
41-3 
51-6 


30.^ 
41.0 
51.2 


30. 
40. 
50. 



65 

6.6 

7.0 

8.6 

9.1 

10. 1 

20.1 

30.2 

40.3 
50.4 



60 

6.0 
7.0 
8.0 
9.0 

lO.O 

20.0 
30.0 
40.0 
50.0 



59 59 





58 


58 


Si 


57 


6 


5-8 


5.8 


s-1 


5- 


7 


6.8 


6.^ 


6.7 


6. 


8 


7.8 


7.1 


7-6 


7- 


9 


8.8 


8.7 


8.6 


8. 


10 


9-1 


9-6 


9.6 


9- 


20 


19.5 


19-3 


19. 1 


19. 


30 


29.2 


29.0 


28.7 


28. 


40 


39-0 


38-6 


38.3 


38. 


50 


48.^ 


48-3 


47-9 


47. 





56 


56 


5S 


55 


6 


5-6 


5.6 


5-5 


5- 


7 


6.6 


6.5 


6.5 


6. 


8 


7-5 


7-4 


7-4 


7- 


9 


8.5 


8.4 


8-3 


8. 


10 


9.4 


9-3 


9.2 


9- 


20 


18.8 


18.6 


18.5 


18. 


30 


28.2 


28.0 


27.^ 


27. 


40 


37-6 


.37-3 


.37-0 


36. 


50 


47.1 


46.6 


46.2 


45- 





54 


3 


6 


5-4 


0.3 


7 


6.3 


0.3 


8 


7.2 


0.4 


9 


8.2 


0.4 


10 


9.1 


0.5 


20 


18.1 


I.O 


30 


27.2 


1-5 


40 


36.3 


2.0 


50 


45-4 


2.5 



2 

0.2 

0.3 

0-3 
0.4 
0.4 

0.8 
1.2 

1-6 
2.1 



p. P. 



IT 



40 



TABLE IV. 



9 
10 

II 

13 

13 
U 

15 
i6 

17 
i8 

19 



20 

21 
22 

23 
_2£ 

25 

26 
27 
28 
29 

30 

31 
32 
33 

34 

35 
36 
37 
38 
39 



40 

41 

42 
43 
44 



45 
46 

47 
48 

49 



50 

51 
52 
53 

54 



55 
56 
57 
58 
59 
60 



I/O!;. Sill. 



35 209 
35 263 
35 318 
35372 
35427 



35481 
35536 
35 590 
35644 
35 698 



35752 
35 806 
35 866 
359'4 
35968 



36 03l 
36075 
36 128 
36 1S2 
3623? 



36289 
36342 
36393 
36448 
36 501 

36554 
36607 
36 660 

36713 
36766 



36818 
36871 

36923 
36976 

37 028 



37 081 
37 133 
37185 
3723? 
37289 



9-37 341 
9-37 393 
9-37 445 
9-37 497 
9-37 548 



9.37 600 
9.37652 
9-37703 
9.37755 
9-37805 



9-37857 

9-37909 
9.37960 
9.3801T 
9.38 062 



9-38 113 
9.38 164 
9.38215 
9.38 266 
9-38 317 

9-3836^ 
Log. Cos. 



54 
54 
54 
5-+ 
54 
54 
54 
54 
54 
54 
54 
54 
53 
54 
53 
53 
53 
53 
53 
53 
53 
S3 
53 
53 
53 
53 
53 
52 
53 
52 
52 
52 
52 
52 
52 
52 
52 
52 
52 
52 
52 
51 
52 
51 
52 
51 
51 
5? 
51 
51 
51 
51 
51 
51 
51 
51 
50 
51 
51 
50 



Log. Tan. 




36336 
36 394 
36451 
36509 

36 566 



36623 
36681 
36738 

3679? 
36852 



36 909 

36 966 
37023 
37080 

37 136 



37 47^ 
37532 
37588 
37644 
37 700 



37 756 
37 812 
37868 
37924 
37 979 



3803^ 
38 091 

38 146 
38 202 

3825? 



38313 
38368 

38423 
38478 
38 533 



38 589 
38644 
38698 

38753 
38808^ 

38863 
38918 
38972 
39027 
39081 



39 136 
39 190 
39244 
39299 
39 353 



3940? 
39461 
39515 
39569 
39623 

9-39677 
Log. Cot. 



c. d. 

S7 
57 
57 
S? 
57 
57 
57 
S? 
57 
57 
57 
56 
57 
56 
57 
5§ 
56 
56 
56 
56 
56 
56 
56 
56 
56 
Si 
56 
56 
55 
56 
5? 
5? 
5? 
5§ 
55 
55 
55 
55 
55 
55 
55 
54 
55 
55 
54 
55 
54 
Si 
54 
54 
54 
54 
54 
54 
54 
54 
54 
54 
54 
53 

c. d. 



13 

Log. Cot. 
0.63 663 
0.63 606 
0.63 548 
0.63 491 
063 433 
0.63 376 
0.63319 
0.63 262 
0.63 204 
0.63 147 



o. 63 096 
0.63033 
0.62 977 
0.62 920 
0.62 863 
0.62 805 
0.62 750 
0.62693 
0.62637 
0.62 580 



0.62 524 
0.62 468 
0.62 412 
0.62356 
0.62 299 



0.62 243 
0.62 188 
0.62 132 
0.62 076 
0.62 020 



0.61 964 
0.61 909 
0.61 853 
o.6r 798 
0.61 742 
0.61 687 
0.61 632 
0.61 576 
0.61 521 
0.61 466 



0.61 41 1 
0.61 356 
o.6r 301 
0.61 246 
0.61 191 



0.61 137 
0.61 082 
0.61 02^ 
0.60973 
0.60 91 8 



0.60 864 
0.60 809 
0.60 755 
0.60 701 
0.60 647 



0.60 592 
0.60 538 
0.60484 
0.60430 
o-6o 376 
0.60 323 

Log. Tan. 



Log. Cos. 
9.9^872 
9.98 861} 
9.98 865 
9.98863 
9.98 860 
9.98 858 
9-98855 
9.98 852 
9.98849 
9. 98 840 
9.98843 
9.98 840 
9.98837 
9.98 834 
9-98831 
9.98 828 
9.98 825 
9.98 822 
9.98 819 
9-98 816 



9.98 813 
9.98 816 
9.98 807 
9.98 804 
9.98 801 

9^798 
9.98795 

9-98792 
9.98789 
9.98786 



9.98783 
9.98 780 
9.98777 
9.98774 
9.98771 



9.98 768 

9-98 765 
9.98 762 
9.98759 
9-98755 



9.98752 
9.98749 
9-98746 
9-98743 
9-98 740 



998737 
9-98734 
9.98731 
9.98728 
9-98725 



9.98 721 
9.98 718 
9.98715 
9.98712 
9-98 709 



9.98 706 
9.98 703 
9.98 700 
9.98696 
9-98693 
9.98 696 

Log. Sin. 



(>0 

59 

58 

57 

_56 

55 
54 
53 
52 

_1L 
50 

49 
48 

47 

45 
44 
43 
42 
41 



40 

39 
38 
37 

35 
34 
33 
32 
31 
30 
29 
28 
27 
26 



25 
24 

23 
22 
21 

"20 

19 
18 

17 
16 

15 
14 
13 
12 
II 
To 

9 

8 

7 
6 



5^ 57 S6 56 



5-? 
6.7 


5-7 
6.6 


5-6 
6.6 


5.6 
6-5 


7-6 
8.6 


7-6 
8.5 


7-5 
8.5 


7-4 
8.4 


9.6 
19.T 
28.^ 


9-5 
19.0 

28.5 


9-4 
18.8 
28.2 


9-3 
18.6 
28.0 


38-3 


38.0 


37-6 


37-3 


47-9 


47-5 


47.1 


46.6 



S5 55 54 



5-5 


5-5 


5-4 


6.5 


6.4 


6-3 


7-4 


7-3 


7.2 


8.3 


8.2 


8.2 


9-2 


9-1 


9-1 


18.5 


18.3 


18. I 


27.7 


27-5 


27.2 


37-<^ 


36-6 


36.3 


46.2 


45-8 


45-4 



S3 


53 


52 


5 
6 


3 


5 
6 


3 



5.2 
6.1 


7 
8 
8 

17 
26 


T 


9 
8 


7 
7 
8 

17 
26 



9 
8 
6 

5 


7.0 
7-9 
8.7 

17-5 
26.2 


35 
44 


6 
6 


35 
44 


3 
I 


35-0 
43-^ 



54 

5-4 

6-3 

7-2 

8.1 

9.0 

18.0 

27.0 

36.0 

45.0 



52 

5-2 

6.0 

6.9 
7.8 

8.6 
17.3 
26.0 

34-6 
43-3 



6 

7 
8 

9 
10 
20 

30 
40 

50 



SI 

5.1 
6.0 

6.8 
7-7 
8.6 
17.T 
25.? 
34-3 
42-9 



SI 
5-1 

5-9 
6.8 

7-6 

8-5 

17.0 

25-5 
34.0 
42.5 



SO 





3 


3 


6 


0.3 


0.3 


7 


0.4 


0.3 


8 


0.4 


0.4 


9 


0.5 


0.4 


10 


0.6 


0.5 


20 


I.I 


I.O 


30 


I.? 


1-5 


40 


2.3 


2.0 


50 


2.9 


2.5 



2 

0.2 

0.3 
0.3 
0.4 
0.4 
0.8 

1.2 

1-6 

2.1 



76= 



41 



14^ 



TABLE IV. 



15 
16 

17 
18 

19 

20 

21 
22 
23 
24 

25 
26 
27 
28 
29 
30 
31 
32 
33 
34 

35 
36 
37 
38 
39 
40 
41 
42 
43 
44 

45 
46 

47 
48 

49 

50 

51 
52 
53 
54 

55 
56 
57 
58 
59 
(>0 



lioy. Sill. 

367 
418 

468 
519 
569 



Log. Tau. 



9-38 
9-38 
9-38 
9.38 
9-38 
9-38 
9-38 
9-38 
9-38 
9-38 
9-38 
9-38 
938 

9-39 
9-39 

9-39 
9-39 
9-39 
9-39 
9-39 
9-39 
9-39 
9-39 
9-39 
9-39 
9-39 
9-39 
9-39 
9-39 
9-39 
9-39 
9-39 
9-39 
9.40 

9- 40 
9.40' 
9.40 
9.40 
9.40 
9-40 
9.40 
9.40 
9.40 
9.40 
9-40 
9.40 
9.40 
9.40 
9.40 
9- 40 
9.40 
9.40 
9.40 
9.40 
9-41 
9.41 
9.41 
9.41 
9.41 
9.41 



620 
676 
726 

771 
821 

871 
921 
971 
021 
071 
126 
176 
220 
269 
3'9 

368 
418 

46? 

516 
566 

615 
664 

713 
762 
811 
860 
909 

957 
006 

055 
103 
152 
206 
249 
297 

345 
394 
442 
490 
538 
586 

634 
682 

730 

n1 
82$ 

873 
926 
968 

OlJ_ 

063 

no 
158 
205 

2 1)2 



9-41 299 
Log. Cos. 



50 
56 
50 
56 
50 
50 
50 
50 
50 

50 
50 
50 
50 
50 
49 
50 
49 
49 
49 
49 
49 
49 
49 
49 
49 
49 
49 
49 
49 
49 
49 
48 
48 
49 
48 



48 
4S 

48 
48 
48 
48 
48 

48 
48 
48 
48 
4? 
48 
47 
47 
4? 
4? 
4? 
4? 
4? 
47 
47 
47 



39677 
39731 
39784 
39838 
39892 



39 945 

39 999 
40052 

40 106 
40 159 



40 212 
40 265 
40318 
40372 

40435 



40478 
40531 
40583 
40636 
40 689 



40742 
40794 
40847 
40 899 
40952 



004 

057 
109 
161 
213 



266 
318 
370 
422 
474 



52? 
57^ 
629 
681 
732 



784 
836 
88^ 

938 
990 



42 041 
42 092 

42 144 
42195 
42246 



4229^ 
42348 
42399 
42456 
42 501 



42552 
42 602 
42653 
42704 
42754 
9.42 805 

Log. Cot. 



c. d. I Log. Cot. 



c. d. 



0.60323 
0.60 269 
0.60 21 § 
0.60 161 
0.60 108 



0.60054 
0.60001 

o. 59 947 
o. 59 894 
0.59 841 



0.59787 
0.59734 
0.59 681 
0.59 628 
o- 59 575 



0.59 522 
o. 59 469 
0.59416 

0.59363 
0.59311 



0.59258 

0.59 20§ 

0.59153 
0.59 106 

o. 59 048 



0-58995 

o. 58 943 
0.58891 
0.58838 
0.58786 



0.58734 
0.58682 
0.58 630 
9.58578 
0.58 526 



0.58474 
0.58 422 
0.58376 
0.58319 
0.5826^ 



0.58 216 
0.58 164 
0.58 112 
0.58061 
0.58C10 



Log. C08. 



0-57 958 
o. 57 90? 
0.57856 
0.57805 
0.57753 



0.57 702 
0.57651 
o. 57 606 

0.57549 
o. 57 499 



0.57448 
0.57397 
0.57 346 
o. 57 296 

0-57245 
0-57 195 

LOK. Tan. 



98 696 
98687 
98684 
98681 
98678 
98674 
98 671 
98668 
98665 
98662 



98658 
98655 
98 652 
98 649 
98646 



98639 
98636 
98633 
98630 



98626 
98623 
98 620 
98617 
98613 



98 616 
98 607 
98 604 
98 606 
9859? 



98 594 
98591 
9858? 
98584 
98 581 



98578 

98 574 
98571 
98 568 
98564 



98 561 
98558 
98554 

98551 
98548 



98 544 
98541 

98538 
98534 
98531 



98528 
98524 
98521 
98518 
98514 



98 511 
98 508 
98504 
98 501 
98498 
9.98494 



CO 

59 
58 
57 

Ji 

55 
54 
53 
52 
_5_L 
50 

49 
48 

47 

45 
44 
43 
42 

41 
40 

39 
38 
37 
Ji 
35 
34 
33 
32 
31 
30 

29 
28 
27 
26 



24 
23 

22 
21 

"20 

19 
18 

17 
16 



15 
14 
13 
12 
II 

lo 

9 
8 

7 
6 





54 


S3 


S3 


6 


5-4 


5-3 


5-3 


7 


6-3 


6.2 


6 


2 


8 


7-2 


7-1 


7 





9 


8.1 


8.0 


7 


9 


10 


9.0 


8.9 


8 


8 


20 


18.0 


17-8 


17 


6 


30 


27.0 


26.5^ 


26 


5 


40 


36.0 


35-6 


35 


3 


50 


45.0 


44.6 


44 


I 





52 


52 


51 


51 


6 


5-2 


5-2 


5.1 


5. 


7 


6.1 


6.6 


6.0 


5. 


8 


7.0 


6-9 


6-8 


6. 


9 


7-9 


7.8 


7-7 


7- 


10 


8.? 


8-6 


8.6 


8. 


20 


17.5 


1 7.. 3 


i7-'i 


17- 


30 


26.2 


26.0 


25.^ 


25. 


40 


35-0 


34-6 


34-3 


34. 


5043-? 


43-3 


42-9 


42. 





56 


50 


49 


49 


6 


5-0 


5.0 


4-9 


4- 


7 


5-9 


5-8 


5-8 


5- 


8 


b.7 


6.6 


6.6 


6. 


9 


7-6 


7-5 


7.4 


7- 


10 


8.4 


8.3 


8.2 


8. 


20 


16.8 


16.6 


16.5 


16. 


30 


25.2 


25.0 


24.? 


24- 


40 


33-6 


33-3 


33-0 


32- 


50 


42.1 


41.6 


41.2 


40. 





48 


48 


Al 


47 


6 


4-8 


4.8 


4.7 


4- 


7 


5-6 


5.6 


5-5 


5- 


8 


6.4 


6.4 


6.3 


6. 


9 


7.3 


7.2 


7-1 


7- 


10 


8.1 


8.0 


7-9 


7- 


20 


16.1 


16.0 


15-8 


15- 


30 


24.2 


24.0 


23-7 


23- 


40 


32-3 


32.0 


31-6 


31- 


50 


40.4 


40.0 


39-6 


39- 



6 

7 
8 

9 
10 
20 

30 
40 

50 



3 

0.3 
0.4 
0.4 

0-5 
0.6 
I.I 
I-? 
2-3 
2-9 



75' 



3 

0-3 
0-3 
0.4 
0.4 
0.5 

I.O 

1-5 
2.0 

2.5 



42 



TABLE IV. 



15^ 



9 
10 
II 

12 
13 
14 

15 
16 

17 
18 

19 



20 

21 

22 

23 

_££ 

25 
26 
27 
28 
29 



30 

31 
32 
33 
34 



35 
36 
37 
38 
39 



40 

41 
42 
43 
44 

45 
46 

47 
48 

49 



50 

51 

52 
S3 
54 

55 
56 
57 
58 
59 
GO 



hog. Sill. 



9-4 
9.4 

9-4 
9.4 

9-4 



9.4 
9.4 
9-4 
9-4 
9-4 



9-4 
9.4 
9.4 
9-4 
9-4 



299 
346 
394 
441 
488 



534 
581 
623 

675 
731 



768 
8.5 
861 
908 
954 



9.42 000 
9.42047 
9.42093 
9.42 139 
9.42 185 



9.43 232 

9.42 278 

942 324 

9.43 369 

942415 



9.42461 
9.42 507 
9-42 553 
9-42 598 
9.42644 



9.42 690 

9-42735 
9.42781 
9.42 826 
9.42871 



9.43917 
9.43 963 
9.43007 
9.43053 
9.43098 



9-43 143 
9.43 188 

9-43 233 
9.43 278 
9-43 322 



9-43367 
9.43412 

9-43 457 
9-43 501 
9-43 546 



9-43 591 
9-4363? 
9.43680 

9-43724 
9-43 768 



9-43813 
9-43857 
9.43 901 

9-43 94? 
9-43 989 
9-44034 

Lo^. Cos. 



47 
47 
47 
47 
46 
47 
47 
46 
46 
47 
46 
46 
46 
46 
46 
46 
46 
46 
46 

46 
46 
46 
4? 
46 
46 
46 
4? 
4? 
46 

45 
4? 
4? 
4? 
45 
45 
4? 
45 
45 
4? 

45 
45 
45 
45 
44 
45 
44 
45 
44 
44 
45 
44 
44 
44 
44 
44 
44 
44 
44 

44' 



LoK. Tan. i c. d. 



9.43 805 
9.42856 
9.42 906 

9-42956 
9.43007 



9-43057 
9.43 107 

9-43 157 
9-43 208 
9.43258 



9-43308 

9-43 358 
9.43408 

9-43458 
9-43 508 



9-43 557 
9.43607 

9.43 657 
9-43 706 
9-43 756 



9-43 806 
9-4385? 
9-43 905 
9-43 954 
9-44003 



9-44053 
9-44 102 

9-44 151 
9.44 200 

9-44249 



9.44299 
9-44 348 
9-44 397 
9.44446 

9-44 49-4 
9-44 543 
9-44 592 
9.44641 
9-44690 
9-44 738 



944787 
9-4483? 
9-44884 
9.44932 
9.44981 



9.45029 

9-4507? 
9.45 126 

9-45 174 
9.45 222 



9-45 270 
9-45 318 
9-45 367 
9.45415 

9-45 463 
9.45510 

9-45 558 
9.45 606 
9.45654 
9-45 702 
9-45 749 

Log. Cot. 



51 
50 
50 
50 
50 
50 
50 
50 
50 
50 
50 
50 
50 
50 

49 
50 
49 
49 
50 
49 
49 
49 
49 
49 
49 
49 
49 
49 
49 
49 
49 
49 
49 
48 
49 
49 
48 
49 
48 
48 
48 
48 
48 
48 

48 
48 

48 
48 
48 

48 
48 
48 
48 
48 

47 
48 
48 
4? 
48 

4f 
77T. 



Lotr. Cut. 

0-57 195 
0.57 144 
0.57094 
0.57043 
o. 56 993 



o. 56 942 
0.56 893 
o. 56 843 
0.56793 
o. 56 743 



o. 56 692 
o. 56 643 
0.56 593 

0.56 542 

o. 56 492 



o. 56 442 

0.56392 

0.56343 
0.56293 

o. 56 243 



0.56 194 
0.56 144 
0.56 095 
o. 56 04? 
0.55 996 



0.55947 
0.55898 

0.55848 
0.55 799 

0-55 750 



0.55 701 
0.55652 
0.55603 

0.55 554 
0.55 50? 



0.55 456 
0.5540? 
0.55 359 
0.55 310 
0.55 261 



0.55 313 
0.55 164 
0.55 116 
0.55067 
0.55019 



0-54970 
0.54 933 
0.54874 
0.5483? 
0.54777 



0.54739 
0.54681 
0.54633 
0.54585 
0.54537 



0.54489 
o. 54 441 
0.54393 
0.54346 
o. 54 298 

0.54250 

Log. Tan. 



Loif. C(i 



9«494 
98491 
98487 

98484 
98481 



9847? 
98474 
98476 
98467 
98 464 



98 466 
98457 
98453 
98450 
98446 



98443 
98439 
98436 
98433 
98439 



98 426 
98 422 
98419 
9841? 
98 412 



98408 
98405 
98 401 
98398 
98 394 



98391 
98387 
98384 
98386 

98377 



90373 
98370 

98366 
98363 
98359 



98356 
98352 
98348 
98345 
98341 



98338 
98334 
98331 
98327 
98324 



98 320 
98316 
98313 
98309 
98306 



98 302 
98298 
98295 
98 291 
98288 
9.98 284 
Log. Sin. 



<>0 

59 
58 
57 
56 



45 
44 
43 
42 
4' 
40 
39 
38 
37 
36 



35 
34 
33 
32 
31 
30 
29 
28 
27 
26 



25 
24 
23 
22 
21 

"20" 

19 
18 

17 
16 



15 
14 
13 
12 
II 

To 

9 

8 

7 
6 



50 50 



6 

7 
8 

9 
10 
20 
30 
40 
50 



5.0 


5- 


5.9 


5- 


6.7 


6. 


7.6 


7- 


8.4 


8. 


16.8 


16. 


25.2 


25- 


33-6 


33- 


42.1 


41. 





49 


49 


48 


6 


4-9 


4-9 


4-8 


7 


5-8 


5-7 


5-6 


8 


6.6 


6.? 


6.4 


9 


7.4 


7-. 3 


7-3 


10 


8.2 


8.T 


8.1 


20 


16.5 


16.3 


16.1 


30 


24.-7 


24.5 


24.2 


40 


33.0 


32.6 


32.3 


50 


41.2 


40.8 


40.4 





41 


47 


4S 


6 


4.1 


4-7 


4-6 


7 


5.? 


5 


5 


5-4 


8 


6.3 


6 


2 


6.2 


9 


7-1 


7 





7.0 


10 


7.9 


7 


8 


1-1 


20 


15-8 


15 


6 


15-5 


30 


23-7 


23 


5 


23.2 


40 


31-6 


31 


3 


31.0 


50 


39-6 


39 


I 


38.? 



4S 

4-! 
5-3 



6.6 
6.8 
7.6 

I5-I 
3022.^ 

40 '30. 3 
5ol37-9 



45 

4-5 
5-2 
6.0 
6.? 

7.5 
15.0 
22.5 
30.0 
37-5 



44 

4.4 



48 

4.8 

5-6 

6.4 

7.2 

8.0 

16.0 

24.0 

32.0 

40.0 

46 

4.6 

5-3 
6.1 

6.9 

7.6 

15-3 

23.0 

30.6 



44 

4.4 
5-i 
5-8 
6.6 

7-3 
14-6 
22.0 

29-3 
36.6 





4 


3 


6 


0.4 


0.3 


7 


0.4 


0.4 


8 


o.S 


0.4 


9 


0.6 


0-5 


10 


0.6 


0.6 


20 


1-3 


i.T 


30 


2.0 


I.? 


40 


2.6 


2.3 


50 


3-3 


2.9 



3 

0-3 
0.3 
0.4 
0.4 
0.5 
i.o 

1-5 
2.0 
2.5 



p. P. 



74c 



43 



16^ 



TABLE IV. 



10 

II 

12 

13 
H 



15 
i6 

i8 
19 



20 

21 

'22 

23 
24 



25 
26 

27 
28 

29 

30 

31 

32 

33 
34 



35 
36 
37 
38 
39 



40 

41 

42 

43 
44 



45 
46 
47 
48 

49 
50 

5' 
52 
53 
54 

55 
56 
57 
58 
59 
«0 



Log. (Sin. 



9.44034 
9-44078 
9.44122 
9.44 166 
9.44209 



9-44 253 
9.44 297 

9-44 34' 
9.44 384 
9-44 428 
9.44472 
9-44515 
9-44 559 
9.44602 
9.44646 



9.44689 
9-44732 
9.44776 
9.44819 
9.44 862 



9-44903 
9-44 948 
9-44991 
9-45034 
9.45077 



9.45 120 
9-45 163 
9.45 206 

9-45 249 
9.45291 



9-45 334 
9-45 377 
9.45419 
9.45462 
9-45 504 



9-45 547 
9.45 589 
9-45631 
9-45 674 
9.45716 



9-45 758 
9.45 800 
9.45 842 
9.45885 
9-45927 



9.45 969 

9.46 01 1 
9.46052 
9.46094 
9-46 136 



9.46 178 
9.46 220 
9.46 261 
9-46 303 
9-46 345 



9.46 386 
9.46428 
9.46469 
9.46 511 
9.46 552 



9-46 593 



Lost. Cos. 



44 
44 
44 
43 
44 
44 
43 
43 
44 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 
42 
43 
43 
42 
42 

43 
42 

42 
42 
42 
42 
42 
42 
42 

42 
42 
42 
42 
42 
42 
42 
41 
42 
42 
41 
42 
41 
41 
42 

41 
41 
41 
41 
41 
41 



d. 



Log. Tail. n. d. 



9-45 749 
9-45 79? 
9-45 845 
9-45 892 
9-45 940 



9.45 98^ 
9.46035 
9.46082 

9.46 129 
9.46 177 



9.46 224 
9.46271 

9-46318 
9.46 366 
9.46413 



9.46 460 
9.46 507 

9-46 554 
9.46 601 
9.4664^ 



9.46694 
9.46741 
9.46 788 
9.46834 
9.46 881 



9.46 928 

9-46 974 

9.47 021 
9.47 o6f 
9.47 114 



9.47 160 
9.47 207 
9-47 253 
9-47 299 
9-47 34§ 



9-47 392 
9-47 438 
9.47484 

9-47 530 
9-47 576 



9.47 622 
9-47 668 
9-47714 
9-47 760 
9.47 806 



9.47851 
9.47 897 

9-47 943 
9.47 989 
9.48034 



9.48 080 

9.48 I2| 
9.48 171 
9-48216 
9.48 262 



9.48 30^ 

9-48353 
9-48 398 
9-48443 
9-48488 



9-48 534 



4? 
47 
47 
4? 
47 
47 
47 
47 
47 
47 
47 
47 
47 
47 
47 
47 
47 
46 
4/ 
47 
46 
46 
47 
46 
46 
46 
46 
46 
46 

46 
46 

46 
46 

46 
46 
46 

46 
46 

46 
46 
4! 
46 
46 

4? 
46 

4§ 
46 

45 
45 
45 
45 
45 
45 
45 
45 
45 
45 
45 
45 



Log. Cot. 



0.54256 

o. 54 202 
0.54155 
0.54 107 
o. 54 060 



0.54012 
0.53965 
0.53917 
0.53870 
0.53823 



0.53776 

0.53728 
0.53 681 

0.53634 
0.53 587 



0.53 540 

0.53493 
0.53446 

0.53 399 
0.53 352 



0.53305 
0.53258 
0.53 212 
0.53 165 
0.53 118 



0.53072 

0.53 02§ 
0.52979 
0.52 932 
0.52886 



0.52 839 
0.52793 
0.52747 
0.52 706 
0.52 654 



0.52 608 
0.52 562 
0.52 516 
0.52 469 
0.52423 



0.52 377 
0.52 33T 
0.52 286 
0.52 240 
0.52 194 



0.52 148 
0.52 102 
0.52 057 
0.52 on 
0.51965 



0.51 920 
0.51 874 
0.51 829 
0.51 783 
0.51 738 



0.51 692 
0.51 647 
0.51 602 

0.51 556 
0.51 511 



o. 5 1 466 



Log. Cot. c. d. I Log. Tau. 



Log. Cos. 



9.98 284 
9.98 286 
9.98 277 
9.98 273 
9.98 269 



9.98 266 
9.98 262 

9.98 258 
9.98255 
9.98251 



9.98 24^ 
9.98 244 
9.98 246 
9-98 236 
9-98233 



9.98 229 
9.98 225 
9.98 222 
9-98218 
9.98 214 



9.98 211 
9.98 207 
9.98 203 
9.98 200 
9.98 196 



9.98 
9.98 
9.98 
9.98 
9-98 



9.98 

9.98 
9.98 
9.98 
9-98 



9.98 
9.98 
9.98 
9.98 
9-98 



9-9« 
9-98 
9.98 
9.98 
9.98 



9-98 
9.98 

9-98 
9-98 
9.98 



9.98 098 
9-98094 
9. 98 096 
9-98086 
9.98 082 



9-98079 

9-98075 
9.98 071 
9.98 06^ 
9.98063 



059 



Log. Sin. 



00 

59 
58 
57 

55 
54 
53 
52 
51 
50 
49 
48 
47 
46 



45 
44 
43 
42 
41 
40 
39 
38 
37 
36 



35 
34 
33 
32 
31 
30 

29 
28 
27 
26 



25 
24 

23 



20 

19 
18 

17 
16 



15 
14 
13 
12 
II 

To 

9 

8 

7 
6 



48 

4-8 

5.6 

6.4 

7.2 

8.0 

16.0 

24.0 

32.0 

40.0 



47 

4.7 
5 " 
6 



47 
4-7 
5 
6 

7 

7 
15 
23 
3' 
39 





46 


46 


4S 


6 


4-6 


4.6 


4.5 


7 


5 


4 


S-3 


5-3 


8 


6 


2 


6.1 


6.6 


9 


7 





6.9 


6.8 


10 


7 


7 


7-6 


7.6 


20 


15 


5 


15-3 


15.1 


30 


23 


2 


23.0 


22.7 


40 


31 





.30.6 


.30.3 


50 


38 


7 


38.3 


37.9 



45 

4-5 
5-2 
6.0 
6.7 

7-5 
15.0 
22.5 
30.0 
37-5 





44 


43 


43 


6 


4-4 


4-3 


4-3 


7 
8 

9 


5-1 
5-8 
6.6 


5-1 
5.8 
6.5 


5.0 
5-7 
6.4 


10 


7-3 


7-2 


7-i 


20 


14-6 


14.5 


14-3 


30 


22.0 


21.7 


21.5 


40 
50 


29-3 
36-6 


29.0 
36.2 


28.6 
35-8 





42 


42 


41 


41 


6 


4.2 


4.2 


4.1 


4- 


7 


4.9 


4-9 


4-8 


4- 


8 


5-6 


5.6 


5.5 


5- 


9 


6.4 


6.3 


6.2 


6. 


10 


7-1 


7.0 


6.9 


6. 


20 


14. 1 


14.0 


13-8 


13- 


30 


21.2 


21.0 


20.^ 


20. 


40 


28.3 


28.0 


27-6 


27. 


50 


35-4 


35-0 


34-6 


34- 



6 

7 
8 

9 
10 
20 

30 
40 

50 



4 

0.4 
0.4 

0.5 
0.6 

o.g 

1-3 
2.0 

2-6 

3-3 



3 

0-3 
0.4 
0.4 
0.5 
0.6 
i.T 
1.7 
2.3 
2.9 



P. P. 



73' 



44 



TABLE IV. 



\T 



oir. Tan. c. <>. I Loif. Cot. 



_4_ 

5 
6 

7 
8 

9 
10 

II 

12 

13 

15 
i6 

17 
i8 

19 

20 

21 



24 



27 
28 



30 

31 
32 
33 
34 

35 
36 
37 
38 
39 
40 

41 
42 

43 

44 

45 
46 

47 
48 

49 

50 

51 

52 
53 
54 

55 
56 
57 
58 
59 
60 



9 47 
9-47 
9-47 
9-47 
9-47 
9-47 

9-47 
9-47 
9-47 
9-47 
9 47 
9-47 
9-47 
9-47 
9-47 
9-47 
9.48 
9.48 
9.48 
9.48 
9-48 
9.48 
9.48 
9.48 
9.48 
948 
9.48 
9.48 
9.48 
9.48 
9-48 
9.48 
9.48 
9,48 
9.48 
9-48 
9.48 
9.48 
9.48 
9.48 
9.48 



593 
635 
676 
717 
758 

799 
846 
88f 
922 
963 
004 
04? 
086 
127 
168 
203 

249 
290 

330 
371 
411 
452 
492 
532 
573 
613 
653 
694 

734 
774 
814 

854 
894 
934 
974 
014 
054 
093 
133 
173 
213 
2 52 
292 

331 
371 
416 
450 
489 

529 
568 

60I 

646 
686 
725 
764 
803 
842 
881 
920 
959 



9-48998 

Log. Cos. 



41 
41 
41 
41 
41 
41 
41 
41 
41 
41 
41 
41 
40 

41 
40 
40 

41 
46 
40 

40 
40 
40 
40 
40 
40 
40 
40 
40 
40 
40 
40 
40 
40 
40 
40 
40 

39 
40 

39 
40 

39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
38 



48534 
48 579 
48 624 
48 669 
48714 



48759 
48 804 
48 S49 
48 894 
48939 



48984 
49023 

49073 
49 118 
49 162 



49207 
49252 
49296 
49341 
4938? 



49430 
49 474 
49518 
49563 
4960^ 



49651 

49695 
49740 
49784 
49828 



49872 

49916 
49 966 
50004 
50048 



50092 
50 136 
50179 
50223 
50 267 



50 31 1 
50354 
50398 
50442 
5048S 



50529 
50572 
50616 
50659 
50 702 



50746 

50789 
50 832 
50876 
50919 



50962 
5100? 
51048 
51 091 
11234 
51 17^ 



9- 

9- 

9- 

9' 
_9 
_9 

Lop. Cot. 



45 

45 
4? 
45 
45 
45 
44 
45 
45 
45 
44 
45 
44 
44 
45 
44 
44 
44 
44 
44 
44 
44 
44 
44 
44 
44 
44 
44 
44 
44 
44 
44 
43 
44 
44 
44 
43 
44 
43 
44 
43 
43 
44 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 



0.51 46b 
0.51 421 
0.51 376 
0.51 336 
0.51 28§ 



0.51 240 
0.51 195 
0.51 151 
0.51 106 
o. 5 1 06 1 



0.51 016 
0.50 971 

0.50926 

0.50 882 

0.5083^ 



0.50 792 
o. 50 748 
o. 50 703 
0.50 659 
0.50 614 



0.50 570 

0.5052? 

0.50 481 

0.50437 

o- 50 392 

o. 50 348 
o. 50 304 
o. 50 260 
0.50 216 
0.50 172 
0.50 128 
o. 50 083 
0.50039 

0.49 996 
0.49952 



0.49 908 
0.49 864 
0.49 826 
0.49 776 
0.49 733 



0.49 689 
0.49 64^ 
0.49 602 
0.49 558 
0.49514 



0.49471 
0.4942? 
0.49 384 
0.49 340 
0.4929? 



0.49254 
0.49 216 
0.49 16? 
0.49124 
0.49081 



0.49 036 
0.48994 
0.48 951 
0.48 903 
0.4886? 



0.48 822 

Log. Tan. 



Lov. Cos. 




98 059 
98 056 
98052 
98 048 
98 044 



98 040 
98036 
98032 
98(028 
98 024 



98 001 

97 99? 
97 993 
97989 

97985 



97981 
97 97? 
97 973 
97969 
97 966 



97 962 
97958 
97 954 
97950 

97946 



97942 
97938 
97 934 
97930 
97 926 



97 922 
97918 

97914 
97910 
97 906 



97 902 
97898 
97894 
97890 
97886 



97881 
9787? 

97873 
97869 
97 86? 



97861 
9785? 
97853 
97849 
97845 
97 841 
97837 
97833 
97829 
97824 



9.97 620 
Log. Sin. 



25 

24 

23 
22 
21 

"20 

19 
18 

17 
16 



15 
14 
13 
12 
II 

To 

9 

8 

7 
6 





4S 


45 


44 


6 


4.5 


4-5 


4-4 


7 


5.3 


5-2 


5-2 


8 


6.0 


6.0 


S-9 


9 


6.8 


6.? 


6.7 


10 


7.6 


7-5 


7-4 


20 


15.1 


15.0 


14.8 


30 


22.7 


22.5 


22.2 


40 


30.3 


30.0 


29-6 


50 


37-9 


37-5 


37-1 



44 

4.4 
5-1 
5-8 
6.6 

7-3 
14-6 
22.0 

29-3 
36-6 



43 43 



6 

7 
8 

9 
10 
20 
30 
40 
50 



4-3 


4- 


5-1 
5.8 

6.5 


5- 
5 
6. 


7.2 


7- 


14.5 


14 


21.7 


21 


29.0 
36.2 


28. 
35- 





41 


41 


40 


6 


4.1 


4.1 


4.0 


7 


4-8 


4.8 


4.7 


8 


5.5 


5.4 


5-4 


9 


6.2 


6.1 


6.1 


10 


6.9 


6.8 


6.? 


20 


13-8 


13-6 


13.5 


30 


20.7 


20.5 


20.2 


40 


27-6 


27-3 


27.0 


50 


34-6 


34.1 


33.^ 



40 

4.0 

4-6 
5-3 
6.0 

6.6 

13.3 
20.0 

26.6 

33-3 



6 

7 
8 

9 
10 

20 
30 
40 
50 



39 

3-9 
4.6 

5-2 

5-9 
6.6 

13-1 
19.? 
26.3 
32-9 



39 

3 
4 
5- 
5- 
6 

13 
19 

26 

32 



38 

3 ' 





4 


4 


6 


0.4 


0.4 


7 


0.5 


0.4 


8 


0.6 


0.^ 


9 


0.7 


0.6 


10 


0.7 


0.6 


20 


1-5 


1-3 


30 


'^ 2 


2.0 


40 


3-0 


2.6 


50 


3.7 


3-3 



3 

0.3 
0.4 
0.4 

0.5 
0.6 
i.T 
I.? 
2-3 
2.9 



1'. P. 



72 



45 



18' 



TABLE IV. 



5 
6 

7 
8 

9 

10 

II 

12 

13 

14 



15 
i6 

17 
i8 

19 



20 

21 
22 
23 

25 
26 
27 
28 
29 



30 

31 
32 
33 
34 



35 
36 
37 
38 
39 



40 

41 

42 
43 
44 



45 
46 

47 
48 

49 



50 

51 
52 
53 
54 

55 

56 
57 
58 
59 



(JO 



Log. Sill. 

9.48 998 

9-49037 
9.49076 

9.49 114 
9-49 153 



9.49 192 
9.49231 
9.49 269 
9.49308 

9-49 346 



949385 
9.49423 
9.49462 
9.49 500 
9-49 539 



9-49 577 
9.49615 

9-49653 
9.49692 

9-49 730 



9.49 768 

9-49 806 
9.49 844 
9.49 882 
9-49920 

9 
9 
9 
9 
9 



49 958 

49 996 
50034 
50072 

50 no 



5014? 
50185 
50223 
50 260 
50298 



50336 

50373 
50 411 

50448 
50486 



50523 
50561 
50598 
5063? 
50 672 



50 710 

50747 
50784 
50 821 
50858 



50895 
50932 

50969 
51 006 

51043 



51 080 
51 117 

51 154 
51 196 
51 22^ 



9.51 264 



Logr. Cos. 



39 
39 
38 
39 
38 
39 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
3? 
38 
38 
3? 
38 
3? 
3? 
38 

3? 
3? 
3? 
3? 
3? 
2>1 
2>1 
37 
3? 
37 
2,1 
37 
3? 
37 
37 
37 
37 
37 
37 
37 
37 
36 
37 
36 
37 
36 



liOi;. Tan. c. d 



9-5 
9-5 
9-5 
9-5 
9-5 



9-5 
9-5 
9-5 
9-5 
9-5 



9-5 
9-5 
9-5 
9-5 
9-5 



9-5 
9-5 

9-5 
9-5 

9-5 



177 
226 
263 
306 
349 



392 
435 
47? 
526 

563 



605 

648 
691 

733 
776 



818 
861 

903 

946 
988 



9.52 030 
9-52073 
9-52 115 
9-52 15? 
9.52 199 



9.52241 
9.52284 
9.52 326 
9.52 368 
9.52410 



9.52452 
9.52494 
9.52536 
9.52578 
9.52 619 



9.52 661 
9-52703 
9-52745 
9.52787 

9.52828 



9.52 870 
9.52 912 
9-52953 
9-52995 
9-53036 



9.53078 
9-53 119 
9-53 161 
9.53 202 

9-53244 



9-53285 

9-53 326 
9-53368 

9- 53 409 
9-53450 



9-53491 
9-53 533 
9-53 574 
9-53615 
9-53656 



9-53697 



Lot?. Cot. 



43 
43 
43 
43 

42 

43 
42 
43 
42 
42 
43 
42 
42 
42 
42 
42 
42 
42 
42 
42 
42 
42 
42 
42 
42 
42 
42 
42 
42 
42 
42 
42 
42 
41 
42 
42 

41 
42 

41 

41 
42 
41 
41 
41 
41 
41 
41 
41 
41 
41 
41 
41 
41 
41 
41 
41 
41 
41 
41 
41 



Loy. Cot. 



0.48 822 
0.48 779 

0.48 736 
0.48 693 
0.48 656 



C. (1. 



0.48 608 
0.48 565 
0.48 522 

0.48 479 
0.48437 



0.48 394 
0.48 351 

0.48 309 
0.48 265 
0.48 224 



0.48 181 
0.48 139 
0.48096 
0.48 054 
0.48 012 



0.47 969 
0.47 927 
0.47 885 
0.47 842 
0.47 800 



0.47 758 
0.47 716 
0.47 674 
0.47 632 
0.47 590 



0.47 548 
0.47 506 
0.47 464 
0.47 422 
0.47 386 



0.47 338 
0.47 296 
0.47 255 
0.47 213 
0.47 17? 



0.47 130 
0.47 088 
0.47 046 
0.47 005 
0-46 963 



0.46 922 
0.46 880 
0.46 839 
0.46 79? 
0.46756 



0.46 714 
0.46 672, 
0.46 632 
0.46 591 
0.46 549 



0.46 508 
0.46467 
0.46 426 
0.46 385 
0.46 344 



0.46 303 



Lo!?. Tan. 



Log. Cos. 



9.97 826 
9.97 816 
9.97 812 

9-97 803 
9-97 804 



9.97 800 

9-97 796 
9.97792 

9-97787 
9-97 783 



9.97 77c, 

9-97 775 
9.97771 

9-97 767 
9-97 763 



9-97 758 
9-97 754 
9-97 750 
9.97746 
9.97 742 



9-97 73? 
9-97 733 
9-97 729 
9-97 725 
9.97721 



9-97 716 
9.97712 
9.97 708 
9.97 704 
9-97 700 



9.97695 
9-97 691 
9-97 687 
9-97 683 
9-97 678 



9-97674 
9.97 670 
9.97 666 
9.97 661 
9-9765? 



9-97653 
9.97649 
9-97 644 
9-97 640 
9-97 636 



9-97632 
9.9762? 
9.97 623 
9-97619 
9.97614 



9.97 616 
9. 97 606 
9.97 601 
9-97 59? 
9-97 593 



9-97 588 
9.97 584 
9.97 580 
9-97 57S 
9-97 571 
9.97 567 



Log:. Sin. 



00 

59 
58 

57 
56 



55 
54 
53 
52 
51 



50 

49 
48 
47 
46 



45 
44 
43 
42 

41 



40 

39 
38 
2>7 
36 



35 

34 
33 
32 
31 



30 

29 
28 
27 
26 



25 
24 
23 
22 
21 



20 

19 
18 

17 
16 



15 
14 
13 
12 
II 



10 

9 

8 

7 
6 



p. p. 





43 


42 


6 


4-3 


4-2 


7 
8 

9 


5-0 

5-? 
6.4 


4.9 
5-6 
6.4 


10 


7-1 


7-1 


20 


14-3 


14.1 


30 
40 


21.5 
28.6 


21.2 
28.3 


50 


35-8 


35-4 



42 

4.2 
4.9 

5-6 

6.3 
7.0 
14.0 
21.0 
28.0 
35-0 





41 


6 


4-1 


7 


4-8 


8 


S-? 


9 


6.2 


10 


6.9 


20 


13-8 


30 


20.7 


40 


27-6 


SO 


34-6 



41 

4-1 
4.8 

5-4 
6.1 

6.8 
13-6 
20.5 

27-3 
34-1 





39 


38 


3i 


6 


3-9 


3-8 


3- 


7 


4-5 


4 


5 


4- 


8 


5-2 


5 


I 


5- 


9 


5-8 


5 


8 


5- 


10 


6-5 


6 


4 


6. 


20 


13.0 


12 


8 


12. 


30 


19.5 


19 


2 


19- 


40 


26.0 


25 


6 


25- 


50 


32.5 


32 


I 


31- 





37 


37 


6 


3-? 


3-7 


7 


4-4 


4-3 


8 


5.0 


4-9 


9 


5.6 


5-^ 


10 


6.2 


6.T 


20 


12.5 


12.3 


30 


18.? 


18.5 


40 


25.0 


24-6 


50 


31.2 


30.8 



36 

3-6 
4.2 

4-8 
5-5 
6.1 
1 2. 1 
18.2 
24-3 
30-4 





4 


6 


0.4 


7 


0.5 


8 


0.6 


9 


0.7 


10 


0.7 


20 


1-5 


30 


2.2 


40 


3-0 


50 


3-? 



p. p. 



71 



4 

0.4 
0.4 
0.5 
0.6 
0.6 
1-3 
2.0 

2-6 

3-3 



46 



TAHLE IV. 



19^ 



Imk. sill. 



5 
6 

7 
8 

9 
10 

1 1 

12 
13 

'4 

15 
16 

17 
iS 

19 



24 



-3 
26 

27 
28 



30 

31 

32 
33 
34 



J3 
36 

37 
38 
39 



40 

41 
42 
43 
44 

45 
46 

47 
48 

49 

50 

51 
52 

53 
54 



55 
56 
57 
58 
59 
(50 



264 
301 
337 
374 
416 



447 
483 
520 

556 
593 



629 
665 
702 
738 
774 



816 

847 
883 
919 
955 



ji 991 
52027 
52063 
52099 
52135 



52 170 
52206 
52242 
52278 
52314 



52349 
52385 
52421 

52456 
52492 



52527 
52563 
52598 
52634 
52 669 



52704 
52740 
5277? 
52 816 
52846 



52881 

52 916 

52951 
52986 
53021 

53056 
53091 

53 126 
53 161 
53 196 



53231 
53266 

53301 
53 33? 
53370 

9-53405 

Lost. Cos. 



0/ 
36 
36 

36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
3l 
36 
36 
35 
36 

35 
3? 
36 
35 
3! 
3? 
3? 
3? 
3> 
3? 
35 
3§ 
3§ 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
34 
35 
35 
34 
35 
34 



o^. Tnii. r. (I. Loir. Cot. 



53 697 
53738 

53 779 
53820 
53861 



53902 
53 943 
53983 
54024 
54065 



54 106 

54147 
54187 
54228 
54269 



54309 
54350 
54390 
54431 
54 471 



54512 
54552 
54 593 
54633 
54673 



54714 
54 754 
54 794 
54834 
54874 



54915 
54 955 
54 995 
55035 
55075 



55 115 
55 155 
55195 
55235 

55275 



55315 
55 355 
55 394 
55434 
55 474 



55 514 
55 553 
55 593 
55633 
55672 



55712 
55751 
55791 
55831 
55870 



55909 
55 949 
55988 
56028 
5606^ 

9-56 log 

Loff. Cot. c. d. 



41 
41 
41 
41 
41 
41 
40 
41 
41 
46 

41 
40 
40 
41 
40 
40 
40 
40 
46 

40 
40 
40 
40 
40 
46 
40 
40 
40 
40 

40 
40 
40 
40 
40 
40 

39 
40 
40 
40 
40 
40 
39 
40 
39 
40 

39 
40 
39 
39 
39 
39 
40 
39 
39 
39 
39 
39 
39 
39 
39 



0.46 303 
0.46 262 
0.46 221 
0.46 180 
0.46 139 



0.46 098 
0.46057 
0.46 016 
0-45 97I 
0.45 934 



0.45 894 

0.45853 
0.45 812 
0.45772 
0.45731 



0.45 690 
0.45 650 
0.45 609 
0.45 569 
0.45 528 



0.45 488 

0.45 447 
0.45 407 
0.45 367 
0.45 326 



0.45 286 
0.45 246 
0.45 205 
0.45 i6| 
0.45 125 



0.45 085 
0.45045 
0.45 005 
0.44 965 
0.44925 



0.44 8S4 
0.44 845 
0.44 805 
0.44765 
0.44725 



0.44 685 
0.44645 
0.44 605 

0.44 565 
0.44 526 



0.44486 
0.44 446 
0.44 406 
0.44 367 

0.44327 



0.44 288 

0.44248 
0.44 208 
0.44 169 
0.44 129 



0.44090 
0.44051 
0.44 01 T 
0.43 972 
0-43 932 

0.43893 
liOir. Tan. 



Imk. Cos. 



97 567 
97 562 
97 558 
97 554 
97 549 



97 545 
97 541 
97 536 
97532 
97 527 
97 523 
97 519 
97514 
97510 

97 505 



97501 
97 497 
97492 
97488 
97483 



97 479 
97 475 
97476 
97466 
97461 



97 457 
97452 
97448 
97 443 
97 439 



97 434 
97430 
9742S 
97421 
97 416 



97412 
97407 
97403 
97 398 
97 394 



97389 
97385 
97386 

97376 
97371 



97367 
97362 

97358 
97 353 
97 349 



97 344 
97340 
97 335 
97330 
97326 



97321 

97317 
97312 
97308 
97303 



9.97 29s 
Log. Sill. 



(>0 

59 
58 
57 
56 



55 
54 
53 
52 
51 
50 

49 
48 

47 
46 



45 
44 
43 
42 
41 
40 
39 
38 
37 
36 



35 
34 
33 
32 
31 
30 
29 
28 
27 
26 



24 
23 
22 
21 

J9 
18 

17 
16 



15 
14 
13 
12 
1 1 

To 

9 

8 

7 
6 





41 


40 


40 


6 


4.1 


4.6 


4.0 


7 


4.8 


4-7 


4-6 


8 


5-4 


5-4 


5-3 


9 


6.T 


6.1 


6.0 


10 


6.8 


6.f 


6.6 


20 


13-6 


•3-5 


'3-3 


30 


20.5 


20.2 


20.0 


40 


27-3 


27.0 


26.6 


50 


34-1 


33-7 


33-3 





39 


6 

7 
8 


3-9 
4.6 

5-2 


9 
10 


5-9 
6.6 


20 


I3-I 


30 

40 


19-7 
26.3 


50 


32.9 



39 

3-9 

4.5 

5-2 

5-8 

6.5 

13.0 

19.5 

26.0 

32.5 





37 


36 


6 


3-7 


3-6 


7 
8 


4-3 
4.9 


4.2 
4.8 


9 
10 


5-5 
6.T 


5-5 
6.1 


20 


12.3 


12. 1 


30 


18.5 


18.2 


40 


24.6 


24.3 


50 


30-8 


30.4 





3S 


35 


6 


3.§ 


3-5 


7 


4.1 


4.1 


8 


4.7 


4-6 


9 


5-3 


5-2 


10 


5-9 


5-8 


20 


II. 8 


II. 6 


30 


17.7 


17-5 


40 


23-6 


23-3 


50 


29.6 


29.1 





5 


4 


6 


0.5 


0.4 


7 


0.6 


0.^ 


8 


0.6 


0.6 


9 


o.f 


0.7 


10 


0-8 


0.7 


20 


1-6 


1-5 


30 


2.5 


2.2 


40 


3-3 


3-0 


50 


4.1 


3.7 



36 

3-6 
4.2 
4.8 

5-4 
6.0 
12.0 
18.0 
24.0 
30.0 



34 

3-4 
4.0 
4.6 
5.2 

S-f 
II. 5 
17.2 
23.0 
28.; 



4 

0.4 
0.4 
o.§ 
0.6 
0.6 

1-3 
2.0 

2-6 

3-3 



70^ 



47 



20^ 



TABLE IV. 



10 

II 

12 

13 

14 

15 
i6 

17 
i8 

19 



20 

21 

22 

23 

24 



25 
26 
27 
28 
29 



30 

31 
32 
33 
34 



35 
36 
37 
38 
39 



40 

41 
42 
43 
44 



45 
46 

47 
48 

49 
50 

51 

52 
53 
54 



55 
56 
57 
58 
59 
00 



Log. Sill. 

9^405 
9.53440 

9-53 474 
9-53509 
9-53 544 



9-53 578 
9-53613 
9-5364? 
9-53682 

9-53 716 

9-53750 
9-53 7S5 
9-53819 
9-53854 
9-53888 

9.53922 

9-53 956 
9-53990 
9-54025 
9.54059 



9-54093 
9.54127 
9.54 16T 

9-54 i9§ 
9.54229 



54263 
54297 
54331 
54365 
54 398 



9-54 432 
9-54466 
9- 54 500 
9-54 534 
9.5456? 



9.54601 

9-54634 
9. 54 668 
9.54702 
9-54 73? 



9.54769 
9. 54 802 
9.54836 
9.54869 
9. 54 902 



9-54936 
9.54969 
9. 5 5 002 
9.55036 
9.55069 



9.55 102 
9-55 i3§ 
9-55 168 
9.55202 

9-55235 



9.55268 
9.55301 
9-55 334 
9-55367 
9-55 400 

9-55 433 

Log. C'o.s. 



35 
34 
34 
35 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
33 
34 
34 
34 
33 
34 
34 
33 
34 
33 
33 
33 
34 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 



Log. Tan. 
9.56 I06 
9.56 146 
9.56185 
9.56 224 
56263 



56303 
56342 
56381 
56420 
56459 



56498 
5653? 
56576 
5661S 
56654 



56693 
56732 
56771 
56810 
56848 



56887 
56 926 

56965 
57003 
57042 



57081 
57 119 
57158 
57196 

57235 



57274 
57312 
57350 
57389 
5742? 



57466 
57504 
57542 
57581 
57619 



5765? 
57696 

57 734 
57772 
57810 



57848 
57886 
57925 
57963 
58001 

58039 
58077 
58115 

58153 
58 190 



58228 
58266 
58304 
58342 
58380 

9-5841? 

Log. Cot. 



c. d. 

39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
39 
38 
39 
39 
39 
39 
38 
39 
38 
39 
38 
38 
39 
38 
38 
38 
38 
39 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
38 
3? 
38 
38 
38 
3? 
38 

— 



Log. Cot. 

0.43 893 
0.43854 

0.43815 
0.4377? 

0-43 736 
0.43697 
0.43658 
0.43619 
0.43 5S0 
0.43 540 



0.43 501 
0.43 462 

0.43423 
0.43 384 
0.43 346 



0.43 307 
0.43 268 

0.43 229 
0.43 190 

0.43 151 



0.43 112 
0.43074 
0.43035 
0.42 996 
0.42 958 



0.42 919 
0.42 880 
0.42 842 
0.42 803 
0.42 765 



0.42 726 
0.42 68? 
0.42 649 
0.42 611 
0.42 572 



0.42 534 
0.42 49§ 
0.4245? 
0.42 419 
0.42 380 



0.42 342 
0.42 304 
0.42 266 
0.42 22? 
0.42 189 



0.42 151 
0.42 113 
0.42 075 
0.42037 
0.41 999 
0.41 961 
0.41 923 
0.41 885 
0.41 847 
0.41 809 



0.41 771 

0.41 733 
0.41 695 
0.41 658 
0.41 620 
0.41 582 

Log. Tan. 



Log. Cos. 



97298 
97294 
97289 
97285 
97 280 



9727? 
97271 
97266 
97 261 
97257 



97252 
97248 
97243 
97238 
97234 



97 229 
97224 
97 220 
97215 
97 216 



97 206 
97 201 



97097 
97 092 



9708? 
97 082 
97078 

97073 
97068 



97 063 
97058 
97054 
97049 
97044 



97039 

97034 
97 029 
97025 
97 020 
9-97015 

Log. Sin. 



00 

59 
58 
57 
J^ 
55 
54 
53 
52 
51 
oO 
49 
48 
47 

45 
44 
43 
42 

41 
40 

39 
38 
37 
36 



35 
34 
33 
32 
31 
30 

29 
28 
27 
26 



25 
24 
23 
22 
21 

"20 

19 
18 

17 
16 



15 
14 
13 
12 
II 

lo 

9 
8 

7 
6 



p. p. 





39 


6 

7 
8 


3.9 
4-6 
5-2 


9 
10 


5-9 
6.6 


20 


13- 1 


30 

40 


19.? 
26.3 


50 


32.9 



39 

3-9 

4.5 
5.2 

5-8 
6-5 
13.0 
19.5 
26.0 
32-5 





38 


3« 


6 


3-8 


3-8 


7 


4 


5 


4-4 


8 


5 


I 


5-0 


9 


5 


8 


5-7 


10 


6 


4 


6.3 


20 


12 


8 


12.6 


30 


19 


2 


19.0 


40 


25 


6 


25.3 


50 


32 


I 


31-6 





35 


34 


34 


6 


3-5 


3-4 


3- 


7 


4-1 


4.0 


3- 


8 


4-6 


4.6 


4- 


9 


5-2 


5-2 


5- 


10 


5-8 


5-? 


5- 


20 


II. 6 


1 1- 5 


II. 


30 


17-5 


17.2 


17- 


40 


23-3 


23.0 


22. 


50 


29.1 


28.? 


28. 



3^ 

3-f 
4-4 
5.0 

5.6 
6.2 
12.5 
18.? 
25.0 
31.2 



6 

7 
8 

9 
10 
20 

30 
40 

50 



6 

7 
8 

9 
10 
20 
30 
40 
50 



0.5 
0.6 
0.6 
o.? 
0.8 

1-6 

2.5 

3-3 
4.1 



33 

3-3 
3-8 
4-4 
4.9 

5-5 
I i.o 
16.5 
22.0 

27.5 



4 

0.4 
0.5 
0.6 
0.7 
o.? 

^•5 

2. 2 

3-0 
3-? 



69^ 



TABLE IV 



21 



19 



,56085 
.56 118 
.56150 
.56 182 
.56214 



56 407 

56439 
,56471 

■ 56503 
.5653^ 



.56567 

• 56599 
,56631 
.56663 
56695 



,56727 
56758 
■ 56 790 
,56822 

.56854 



,56885 
.5691? 
56 949 
. 56 980 
49 9-57012 



■ 57 043 

• 57075 

• 57 106 

■ 57138 

• 57 169 



.57 201 
•57232 
.57263 

■ 57295 

■ 57326 



•57 357 



Log:. Co.s. (1 



5«4>7 
58455 
58493 
58531 
585_68_ 
58 606 

58644 
58681 
58719 
58756 



58794 
58831 
58869 
58906 
58944 



58 981 
59019 
59056 
59093 

59 131 



59 168 
59205 
59242 
59 280 
59 317 

59 35 + 
59391 
59 428 
59465 
59502 



59540 

59 577 
59614 
59651 
59688 



59724 
59761 
59 798 
59835 
59872 



59909 
59946 
59982 
60019 
60056 



60093 
60 129 
60 165 
60 203 
60 239 



60 276 
60 312 
60349 
60 386 
60422 



60459 
60495 
60 531 
60568 
60604 



9.60641 



3l 
3f 
38 
37 
37 
3f 
37 
3f 
37 
37 
3l 
3l 
3J 
37 
3l 
3? 
37 
3f 
37 
37 
37 
37 
37 
37 
37 
37 
37 
37 
37 
37 
37 
36 
37 
37 
37 
36 
37 
37 
36 
37 
36 
37 
36 
37 
36 
36 
36 
36 
37 
36 
36 
36 
36 
36 
36 
36 
36 



I.Otf. Cot. 

0.4J 5S2 

0.41 544 
0.41 507 
0.41 469 
0.41 43T 



0.41 394 
0.41 356 
0.41 318 
0.41 2S1 
0.41 243 



0.41 206 
0.41 163 
0.41 131 
0.41 093 
0.41 056 



0.41 018 
0.40 98 1 
0.40944 
0.40 906 
0.40 S69 



0.40 832' 
0.40 794 
0.40757 
0.40 720 
0.40683 



0.40 646 
0.40 608 
0.40 571 
0.40 534 
0.40 497 



0.40 460 
0.40 423 
0.40 386 
0.40 349 
0.40312 



0.40 275 
0.40 238 
0.40 201 
0.40 164 
0.40 128 



0.40 091 
0.40054 
0.40017 
0.39 986 
0.39944 



o. 39 907 
0.39876 
0.39833 
0.39797 
0.39760 



0.39724 
0.3968? 
0.39650 
0.39614 

0.39577 



0.39541 
0.39504 
0.39468 
039432 
0.39395 



0.39359 



Lot;. Cot. c. (I. : Loir. Tim. 



1.01;. Cos. 
9.97015 
9.97 016 
9.97005 
9. 97 000 

9^96^9j_ 
9.96991 
9.96 986 
9.96 981 
9.96976 
9-96971 



9.96966 
9.96 961 

9-96956 
9.96952 

9-96947 



9.96942 

9-96937 
9.96932 
9.96927 
9.96 922 



9.96917 
9.96 912 
9.96907 
9.96 902 
9.96897 



9.96 892 
9.96887 
9.96882 
9.96877 
9.96873 



9.96868 
9.96 863 
9.96858 
9.96853 
9.96 848 



9.96 843 
9.96838 

9-96833 
9.96828 
9.96823 



9.96 818 
9.96 813 
9.96808 
9.96 802 
9.96797 



9.96792 
9.9678? 
9.96 782 
9.9677? 
9.96 772 



9.96767 
9.96 762 

9.9675? 
9.96752 

9.96747 



9.96742 
9-96737 
9-96732 
9.96727 
9.96 721 



716 



<>0 

59 
58 
57 
56 



55 
54 
53 
52 
5' 
50 
49 
48 
47 
46 



45 
44 
43 
42 
41 
40 
39 
38 
37 
36 



35 
34 
33 
32 
31 
30 

29 
28 
27 
26 



-3 
24 
23 
22 
21 

"20 

19 
18 

17 
16 



15 

14 

f3 
12 
II 

To 

9 

8 

7 
6 

5 
4 
3 
2 
I 

~0 





38 


37 


37 


6 


3-8 


3-f 


3- 


7 


4.4 


4.4 


4- 


8 


5-0 


5.0 


4- 


9 


5-7 


5.6 


5- 


10 


6. .3 


6.2 


6. 


20 


12.6 


12.5 


12. 


30 


19.0 


18.? 


18. 


40 


25-3 


25.0 


24. 


50 


31-6 


31.2 


30. 





36 


6 


3-6 


7 


4.2 


8 


4.8 


9 


5-5 


10 


6.1 


20 


12.1 


30 


18.2 


40 


24-3 


50 


30.4 



36 

3-6 

4-2 
4.8 

5-4 
6.0 
12.0 
18.0 
24.0 
30.0 





33 


32 


32 ; 


6 


.3-3 


.3-2 


3-2 j 


7 


3-8 


3.8 


3-7 


8 


4.4 


4-3 


4.2 1 


9 


4-9 


4-9 


4.8 ] 


10 


5-5 


5-4 


5-3 


20 


II. 


10.8 


10.6 


30 


16.5 


16.2 


16.0 


40 


22.0 


21.6 


21.3 


50 


27.5 


27.1 


26.6 





31 


6 


3-1 


7 


3-7 


8 


4.2 


9 


4-7 


10 


5-2 


20 


10.5 


30 


15-7 


40 


21.0 


50 


26.2 



31 

3-1 
3-6 
4.1 

4.6 

5-1 

10.3 

15-5 
20.6 
25-8 





S 


5 


4 


6 


0.5 


o.S 


0.4 


7 


0.6 


0.6 


0.5 


8 


0.7 


0.6 


0.6 


9 


0.8 


0.7 


0.7 


10 


0.9 


0.8 


0.7 


20 


1-8 


1-6 


1-5 


30 


2.7 


2-5 


2. 2 


40 


3-6 


3-3 


3-0 


50 


4.6 


4.1 


3.7 



68^ 



49 



22 



9 
10 

1 1 

12 

u 



15 

16 

17 
18 

19 



20 

21 

22 

23 
24 



25 
26 

27 
28 
29 



30 

31 
32 
33 
34 



35 
36 
37 
38 
39 



40 

41 
42 

43 
44 



45 
46 

47 
48 

49 



50 

51 
52 
53 
54 

55 
56 
57 
58 
59 
60 



57 35? 
57389 
57420 

57451 
57482 

57 513 
57 544 
57576 
57607 
57638 



57669 
57700 

57731 
57762 

57792 



57823 

57854 
57885 
57916 
57 947 



57 977 
58008 
58039 

58 070 
58 100 



58 131 
58 162 
58 192 
58223 
58253 



58284 
58314 
58345 
5837? 
58406 



58436 
58466 

58497 
58527 

58557 



58587 
58618 
58648 
58678 
58708 



58738 
58769 

58799 
58829 

58859 



58889 
58919 
58949 
58979 
59009 



9 
9 
9 
9 
9_ 

9 

JiOg. Cos. 



59038 
59068 

59098 
59128 

5 9158 

59 188 



31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
30 
31 
31 
31 
30 
31 
30 
31 
30 
31 
30 
30 
31 
30 
30 
30 

30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
29 
30 
30 
29 
30 
30 



9.60 641 
9.6067^ 
9.60713 
9.60 750 
9.60785 



9.60 822 
9.60 859 
9.60 895 
9.60931 
9.60 96^ 



9.6 
9.6 
9.6 
9.6 
9.6 



9.6 
9.6 
9.6 
9.6 
9.6 



9.6 
9.6 
9.6 
9.6 
9.6 



9.6 
9.6 
9.6 
9.6 
9.6 



9.6 
9.6 
9.6 
9.6 
9.6 



9.6 
9.6 
9.6 



003 

039 
076 
112 
148 



184 
220 
256 
292 
32S 



364 
400 

436 

472 

50? 



543 
579 
615 
651 

686 



758 

794 
829 
865 



901 

936 
972 



9.62 007 
9.62043 



9.62078 
9.62 114 
9.62 149 
9.62 185 
9.62 220 



9.62 256 
9.62 291 
9.62 327 
9.62 362 
9.62 39^ 



9-62 433 
9.62468 
9.62 503 
9.62 539 
9.62 574 



9.62 609 
9.62 644 
9.62 679 
9.62 715 
9.62 750 



9.62 785 



Lost. Cot. c. <I 



36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
35 
36 
36 
3? 
36 
35 
36 
35 
36 
35 
35 

36 

35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 



o- 39 359 
0.39322 

0.39286 
0.39 250 
0.39213 



0.39 ^n 

0.39 141 
0.39 105 
0.39069 
0.39032 



0.38996 
o. 38 960 
0.38 924 
0.38888 
0.38852 



0.38816 
0.38 780 
0.38744 
0.38 708 
0.38672 



0.38636 
0.38 600 

0.38 564 
0.38 528 
0.38492 



0.38456 
0.38 420 
0.38385 
0.38 349 
0.38 313 



0.38277 
0.38 242 
0.38 206 
0.38 176 
0-38 135 



0.38099 
0.38 063 
0.38028 
0.37 992 
0.37 957 



0.37921 
0.37 886 
0.37 850 
0.37815 
0.37 779 



0-37 744 
0.37 708 

0-37673 
0-37637 
0.37 602 



0.37 567 
0.37 531 
0-37 496 
0.37461 

0.37426 



0.37390 

o- 37 355 
0.37320 
0.37 285 
0.37250 



9-96716 
9.96 71 1 

996706 
9.96 701 
9.96696 



9.96 691 
9.96686 
9.96 681 
9.96675 
9.96 676 



0-37215 
\m^. Tan. 



9.96 665 
9. 96 660 
9-96655 
9.96 650 
9.96644 



9.96639 
9.96634 
9.96 629 
9.96 624 
9.96 619 



9.96 613 
9-96608 
9. 96 603 
9.96598 

9.96 593 



9.9658? 
9.96 582 
9.96577 
9-96 572 
9.96 567 



9.96 561 

9.96 556 
9.96551 
9.96546 
9.96 546 



9-96 535 
9.96 530 
9.96525 
9.96519 
9.96514 



9.96 509 

9-96 503 
9.96498 
9.96493 
9.96488 



9.96482 

9-9647? 
9.96472 
9.96466 
9.96461 



9.96456 
9.96456 

996445 
9.96440 
9.96434 



9-96429 
9.96424 

9-96418 
9.96413 
9. 96 408 



9.96 402 

I;0^. Sill. 



GO 

59 
58 
57 
56 



55 
54 
53 
52 
51 
50 
49 
48 
47 
46 



45 
44 
43 
42 
41 



40 

39 
38 
37 
36 



35 
34 
33 
32 
3' 
30 

29 
28 

27 
26 

~^ 
24 

23 

22 
21 

19 
18 

17 
16 



15 
14 
13 
12 
1 1 

lo^ 

9 
8 

7 
6 





38 


6 


3-6 


7 


4.2 


8 


4.8 


9 


5-5 


10 


6.1 


20 


12. 1 


30 


18.2 


40 


24-3 


50 


30-4 





3S 


6 


3-5 


7 


4-1 


8 


4.? 


9 


5-3 


10 


5-9 


20 


II. 8 


30 


17-? 


40 


23-6 


50 


29.6 





3i 


6 


3-1 


7 


3-7 


8 


4.2 


9 


4.7 


10 


5-2 


20 


10.5 


30 


I5-? 


40 


21.0 


50 


26.2 





30 


30 


6 


3.0 


3-0 


7 


3-5 


3-5 


8 


4.0 


4.0 


9 


4.6 


4-5 


10 


5-1 


5.0 


20 


10. 1 


lO.O 


30 


15.2 


15.0 


40 


20.3 


20.0 


50 


25.4 


25.0 



6 

7 
8 

9 
10 
20 

30 
40 
50 



TABLE IV. 



36 

3-6 
4.2 
4.8 

5-4 
6.0 
12.0 
18.0 
24.0 
30.0 



35 

3-5 
4.1 

4-6 
5-2 
5-8 
II. 6 
17-5 
23-3 
29.1 

31 

3-1 
3-6 
4-i 
4.6 
5-1 
10.3 

15-5 
20.6 

25-8 



29 

2.9 

3-4 

3-9 

4.4 

4-9 

9-8 

14.? 

19.6 

24.6 



5 

0.5 
0.6 
0.6 
o.? 
0.8 
1-6 
2.5 

3-3 
4-1 



I 

0-5 
0.6 

0-? 

0.8 
0.9 
1-8 

2-? 
3-6 
4.6 



P. P. 



67' 



TABLE IV. 



23 



10 

II 

12 

13 
14 



15 
i6 

17 
i8 

19 



20 

21 

22 

23 
24 



25 
26 

27 
28 



30 

31 

32 
33 
34 



35 
36 
37 
38 
39 



40 

41 
42 
43 
44 



45 
46 

47 
48 

49 
50 

51 

52 
53 
54 

55 
56 
57 
58 
59 
60 



Log. Sill. 

9.59 1S8 
9.59217 
9.59247 
9.59277 

9- 59 306 

9 

9 

9 

9 

9 



59 336 
59366 

5939I 
59425 
59 454 



59484 
59513 
59 543 
59572 
59602 



59631 
59661 
59690 
59719 
59 749 



59 778 
59807 

59837 
59866 

59895 



9.59924 

9-59 953 
9.59982 
9.60012 
9.60 041 



9.60070 
9.60099 
9.60 128 
9.60157 
9.60 186 



9.60 215 
9.60 244 
9.60273 
9.60 301 
9.60336 



9.60359 
9.60388 
9.60417 
9.60445 
9-60474 



9.60 503 
9.60532 
9.60 566 
9.60 589 
9.60618 



9.60646 
9.60675 
9.60703 
9.60732 
9.60 766 



9.60 789 
9.60817 
9.60 846 
9.60 874 
9-60903 

9-60931 
Log. Cos. 



29 
30 
29 
29 

30 
29 
29 
29 
29 

29 
29 
29 
29 
29 
29 
29 
29 
29 

29 

29 

29 
29 

29 
29 

29 
29 

29 
29 
29 
29 

29 
29 
29 
29 

29 
29 
29 
28 

29 
29 

28 

29 

28 

29 

28 

29 

28 
28 

29 

28 
28 
28 
28 
28 



28 
28 
28 



Log. Tnii. 

9.62785 

9.62 826 

9.62855 

9.62 896 
9.62 925 



9.62 966 
9-62 99§ 

9.63036 
9.63065 

9.63 io5 



963 i3§ 

9.63 176 

9.63 205 

9-63 240 
9-63 275 



9.63310 

9-63 344 
9-63 379 
9.63414 
9.63449 



9.63484 
9-63518 
963553 
9.63 588 
9.63622 



9.63657 
9.63 692 

9-63726 
9.63761 

9-63795 



9.63 830 
9.63 864 
9.63899 

9-63933 
9.63 968 



9.64 002 
9-64037 
9.64071 
9.64 106 
9.64 146 



9.64174 
9. 64 209 

9.64243 
9.64 27^ 
964312 



9-64 346 
9.64 386 
9.64415 
9.64 449 
9.64483 



9-645'? 
9.64551 

9-64 58 s 

9.64620 

9.64654 



9.64688 

9.64 722 

9.64756 
9.64796 

9.64824 

9-64858 



c. d. 

35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
34 
35 
35 
34 
35 
35 
34 
35 
34 
34 
35 
3-4 
34 
35 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 

Log. Cot. p. (1. 



I/Og. Cot. 
0.37215 
0.37 179 
0.37 144 
0.37 109 
0.37074 



0.37039 
0.37004 
0.36 969 
0.36934 

o. 36 899 



o. 36 864 
0.36 829 

0.36794 

0.36 760 

0.36725 



0.36 690 

0.36655 

0.36 626 

0.36 585 
0.36 551 



0.36 516 
0.36 481 

0.36447 

0.36 412 

0.36377 



Log. Co.s. 
9.96 402 
9.96397 
9.96 392 
9.96 385 
9.96381 



9-96 375 

9.96 376 
9-96365 
9-96359 
9-96354 



9-96349 
996343 
9-96338 
9.96332 

9-96327 
9-96321 
9-96 3I6 
9.96 31 1 
9.96305 
9.96300 



0.36 343 
0.36308 
0.36273 
0.36239 
o. 36 204 



0.36 170 
0.36 135 
0.36 lOI 

0.36066 

0.36 032 



0-3599? 
0-35963 
0.35928 
0.35894 

0.35859 



0.35825 
0.35791 

0.35 756 
0.35 722 
0.35688 



0.35653 
0.35619 

0.35 585 
0.35551 
0.35 517 



0.35482 
0.35 448 
0.35414 
0.35380 

0.35346 



0.35312 
0.35 278 

0.35 244 
0.35209 

0.35 175 

0.35 Ui 

Log. Tnn. 



9.96294 
9.96 289 
9.96 283 
9.96 278 
9.96 272 



9.96 267 
9.96 261 
9.96 256 
9.96 251 
9.96245 



9.96 240 
9.96234 
9.96 229 
9.96223 
9.96 218 



9. 96 2 1 2 
9-96 206 
9.96 201 
9.96 195 
9.96 190 



9.96 184 

9-96 179 
9.96 173 
9.96 168 
9.96 162 



9.96 157 

9.96151 
9.96 146 
9.96 140 
9.96 134 



9.96 129 
9.96 123 
9. 96 118 
9.96 112 

9.96 log 



9.96 lOI 
9.96095 
9. 96 090 
9. 96 084 
9.96078 
9.96073 
Log. Sin. 



(;o 

59 
58 
57 
J6. 
55 
54 
53 
52 
51 
oO 

49 
48 

47 
_46 

45 
44 

43 
42 

_li 
40 

39 
38 
V 
J^ 
35 
34 
33 
32 
31 
30 

29 
28 

27 
26 



25 
24 
23 
22 
21 

19 
18 

17 
16 



15 
14 
13 
12 
II 

To 

9 

8 

7 
6 





Z% 


35 


6 


3.5 


3.5 


7 


4.1 


4.1 


8 


4.? 


4-6 


9 


5-3 


5.2 


10 


5.9 


5-8 


20 


II. 8 


II. 6 


30 


17.? 


17-5 


40 


23-6 


23.3 


50 


29.6 


29.1 



6 

7 
8 

9 
10 

20 

30 
40 

50 



34 34 



30 



6 


3-0 


7 


3-5 


8 


4.0 


9 


4-5 


10 


S-o 


20 


lO.O 


30 


15.0 


40 


20.0 


50 


25.0 



6 

7 
8 

9 
10 

20 
30 
40 
50 



29 

2-9 
3 ' 
3 



29 

2.9 

3 

3 

4 

4 

9 
14 
•9 
24 



28 

2 

3 

3 

4 

4 

9 
14 
19 



6 


6 

0.6 


0.^ 


7 
8 


0.7 
0.8 


0.6 

0.1 


9 
10 


0.9 

I.O 


0.8 
0.9 


20 


2.0 


1.8 


30 

40 

50 


3-0 

4.0 
5.0 


2.? 
3-6 
4.6 



5 

0.5 
0.6 

0.6 
0.1 
0.8 
1.6 
2.5 

3.3 

4.1 



r. iv 



66^ 



51 



24^ 



TABLE IV 



10 

II 

12 
13 

14 



15 
16 

18 
19 



20 

21 

22 

23 
24 



25 
26 
27 
28 
29 



30 

31 
32 
33 
34 



35 
36 
37 
38 
39 



40 

41 
42 

43 
44 



45 
46 

47 
48 

49 



50 

51 
52 
53 
54 

55 
56 
57 
58 
59 
GO 



Log. Sin. 



9.60 93 T 
9.60959 
9.60 988 
9.6 
9.6 



9.6 
9.6 
9.6 
9.6 
9.6 



9.6 
9.6 
9.6 
9.6 
9.6 



9.6 
9.6 
9.6 
9.6 
9.6 



9.6 
9.6 
9.6 
9.6 
9^ 
9.6 
9.6 
9.6 
9.6 
9.6 



9.6 
9.6 
9.6 
9.6 
9.6 



9.6 
9.6 
9.6 
9.6 



OI6 
044 



073 

lOI 

129 

157 
186 



214 
242 
270 
298 
326 



354 
382 
410 
438 
466 



494 

522 

550 
578 
606 



634 
661 
689 
717 
745 



772 
800 
828 
856 



911 

938 
966 

994 



9.62 021 



9.62 049 
9.62076 
9.62 104 
9.62 13T 
9.62 158 



9.62 186 
9.62 213 
9.62 241 
9.62 268 
9.62 295 



9.62323 
9.62 350 
9-6237? 
9.62 404 
9.62432 



9.62459 
9.62485 
9.62513 
9.62 540 
9.62 56? 



9.62 595 



Log. Cos. 



d. 

28 
28 
28 

28 



28 

28 

28 
28 
28 
28 
28 
28 
28 
28 

2f 
28 
28 
28 
2f 
28 
2? 
28 

27 
28 
2f 
28 
2? 
2? 
2? 
2f 
28 
2f 
2f 
27 
27 
2? 
27 
2? 
27 
27 
27 
27 
27 
27 
27 
27 
27 

27 
27 
27 
27 
27 
27 



Log. Tan. 

9.64858 
9.64 892 
9.64925 
9. 64 960 
9-64994 



9.65 02„ 
9.65 062 
9.65 096 
9.65 129 
9-65 163 
9.65 19? 
9.65 231 
9.65 265 
9.65 299 
9-65 332 

9-65 366 
9.65 400 

9-65433 
9.65 467 

9-65 501 

9-65 535 
9.65 568 
9.65 602 
9.65635 
9.65 669 



c. d. 



9.65 703 

9-65 736 
9.65 770 
9.65 803 
9-65 837 
9.65 876 
9.65 904 

9-65 937 

9.65 971 

9.66 004 
9.66 03? 
9.66071 
9.66 104 
9.66 13^ 
9.66 171 



9.66 204 
9.66 23? 
9.66 271 
9.66 304 
9^33^ 



9.66376 
9.66404 

9-66437 
9.66 470 
9-66 503 
9-66 536 
9.66 570 
9.66 603 
9.66636 
9.66669 



9.66 702 
9.66735 
9.66768 
9.66 801 
9.66 834 

Log. Cot. 



34 
34 
33 
34 
34 
34 
34 
33 
34 
34 
33 
34 
34 
33 
34 
33 
33 
34 
33 
34 
33 
33 
33 
33 
34 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
cTdT 



I Log. Cot. 



0.35 141 
0.35 107 
0.35073 
0.35 040 
0.35 006 



0.34972 
0-34938 
0.34904 
0.34 876 
0.34835 



o. 34 802 
0.34769 

0.34735 
0.34701 
0.34667 



0.34633 
o. 34 600 

0.34566 
0.34532 

0.34499 



0.34465 
0.34431 

0.34398 
0.34364 
0.34331 
0.34297 
0.34263 
0.34 230 

0.34 196 
0.34163 



Log. Cos. 



9.96073 
9. 96 06^ 
9. 96 062 
9.96056 
9.96056 



9.96045 
9.96039 
9.96033 
9.96028 
9.96 022 



9-96015 
9.96 oil 
9.96005 

9-95 999 
9.95994 



9.95 988 
9.95982 

9-95 977 
9.95971 
9.95 965 



0.34 129 
0.34096 
o. 34 062 
0.34029 
0.33996 



0.33 962 
0.33929 
0-33895 
0.33862 
0.33829 



0.33795 
0.33762 
0.33729 
0.33696 
0.33662 



0.33629 
0.33 596 
0.33 563 
0.33 529 
0-33 496 



9-95 959 
9-95 954 
9-95 948 
9.95942 

9-95 937 



9-95931 
9.95925 
9.95919 
9.95914 
9-95908 
9.95 902 
9-95 896 
9-95 891 
9-95885 

9-95 879 



9-95873 
9-95 867 
9.95 862 
9-95856 
9-95850 



9-95 844 
9-95 838 
9-95833 
9.95827 
9.95821 



0.33463 
0.33430 
0.33397 
0.33 364 
0.33331 



0.33 298 
0.33265 
0.33232 
0.33 198 
0.33 165 



0.33 132 

Log. Tan. 



9.95815 
9.95809 
9.95 804 

9-95 798 
9-95792 



9-95785 
9.95786 

9-95 774 
9-95 768 
9-95763 



9-95 757 
9-95751 
9-95 745 
9-95 739 
9-95 733 



9-95727 

Log. Sin. 



00 

59 
58 
57 
56 



55 
54 
53 
52 
51 



50 

49 
48 
47 
46 



45 
44 
43 
42 
41 



40 

39 
38 
37 
36 



35 
34 
33 
32 
31 



30 

29 
28 
27 
26 



25 
24 



20 

19 
18 

17 
16 



15 

H 
13 
12 
II 



10 

9 
8 

7 
6 



P. P. 



6 

7 
8 

9 
10 
20 
30 
40 
50 



34 

3-4 

3-9 

4-§ 

5-1 

5-6 

11-3 

17.0 

22.6 

28.3 



33 33 



9 
10 

20 
30 
40 
50 



6 

7 
8 

9 
10 
20 
30 
40 
50 



28 28 



2-8 


2. 


3-3 


3- 


3-8 


3- 


4-3 


4- 


4-7 


4- 


9-5 


9- 


14.2 


14. 


19.0 


18. 


23-7 


23- 





27 


6 


2.7 


7 
8 


3-2 

3-6 


9 
10 


4-1 
4-6 


20 


9-1 


30 
40 


13-7 
18.3 


50 


22.9 



27 

2.7 

3-1 

3-6 
4.6 

4-5 
9.0 

13-5 
18.0 
22. 5 



6 


B 


0.6 


0.5 


0.7 


0.6 


0.8 


0.7 


0.9 


0.8 


I.O 


0.9 


2.0 


1-8 


3.0 


2.7 


4.0 


3-6 


5.0 


4.6 



p. p. 



65' 



52 



TABLE IV. 



25^ 



9 
10 

II 

12 

13 

14 

15 
i6 

17 
i8 

19 



20 

21 
22 

23 
24 

25 

26 
27 
28 
29 



30 

31 

32 
33 
34 

35 
36 
37 
38 
39 



40 

41 

42 

43 
44 



45 
46 

47 
48 
49 
50 
51 
52 
53 
54 

55 
56 
57 
58 
59 
60 



liOff. Sill. 



9.62 595 
9.62 622 
9.62 649 
9.62 676 
9.62703 



9.62 730 
9.62757 
9.62 784 
9.62 81 I 
9.62 838 



9.62 864 
9.62 891 
9-62918 
9.6294? 
9.62972 



9.62999 
9.63025 
9.63052 
9.63079 
9.63 106 



9-63 132 
9.63159 
9.63 186 
9.63 212 
9-63 239 



9.63 266 
9.63 292 
9-63 319 
9-63345 
9.63372 



9-63398 
9.63425 

9-63451 
9.63478 
9.63 504 



9.63 530 
9-63557 
9-63 583 
9.63609 
9.63636 



9.63 662 
9.63688 
9.63715 
9-63 741 
963767 

9-63793 
9.63819 
9.63 846 
9.63 872 
9.63898 



9.63 924 
9.63950 

9-63 976 
9.64002 

9.64028 



9.64054 
9.64080 
9.64 106 
9.64132 
9-64 158 
9.64 184 
Log. Cos. 



27 
27 

27 
27 
27 
27 
27 
27 
27 
26 

27 
27 
27 

26 

27 

26 

27 

26 

27 

26 

27 

26 
26 
26 

27 

26 
26 
26 
26 
26 
26 
26 
26 

26 

26 
26 
26 

26 

26 
26 

26 

26 

26 

26 

26 
26 

26 

26 
26 
26 

26 

26 
26 
26 
26 
26 
26 
26 
26 

25 



Loif. Tun. <'. il. 



9.66 867 
9. 66 900 

9-66933 
9. 66 966 
9.66999 



9.67032 
9.67 065 
9.67097 
9-67 130 
9-67 163 



9-67 196 
9.67 229 
9.67 262 
9.67 294 
967327 



9.67 360 

9-67 393 
9.67425 

9-67 458 
9.67 491 



9.67 523 

9-67 55§ 
9.67 589 
9.67 62I 
9.67654 



9.67 687 
9.67719 
9-67752 
9.67784 
9-67817 



9.67849 
9.67 882 
9.67914 

9-67 947 
9.67979 



9.68 012 
9.68 044 
9.68077 
9.68 109 
9.68 14T 



9.68 174 
9.68 205 
9-68 238 
9.68 271 
9-68 303 



9-68 33§ 
9.68 368 
9.68 400 
9.68 432 
9.68 464 



9.68497 
9.68 529 
9.68 561 
9.68 593 
9.68 62S 



9.6865? 
9.68 690 
9.68 722 

9-68754 
9.68 786 

9.68818 

Log. Cot. I c. d. 



32 

33 
33 
33 
33 
33 
32 
33 
33 
33 
32 
33 
32 
33 
32 
33 
32 
33 
32 

32 
33 
32 
32 
33 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 
32 



Log. Cot. 



0.33 132 
0.33 100 
0.33067 

0.33034 
0.33001 



0.32 968 

0.32 935 
0.32 902 
0.32 869 
0.32836 



0.32803 
0.32 771 
0.32738 
0.32 7o§ 
0.32 672 



0.32 640 
0.32 607 
0.32 574 
0.32 541 
0.32 509 



0.32476 
0.32443 
0.32 411 

0.32 378 
0.32 34! 



0.32 313 
0.32 286 
0.32 248 
0.32 215 
0.32 183 



0.32 150 
0.32 118 
0.32 o8f 
0.32053 
0.32 020 
^88" 
95! 
923 
891 

858 



0.3 
0-3 
0.3 
0.3 
0.3 



0.3 
0.3 
0.3 
0.3 
0.3 



0.3 
0-3 
0.3 
0.3 
0.3 



0.3 
0.3 
0.3 
0.3 
0-3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 



826 

793 
761 

729 
696 



664 
632 
600 

56? 

53? 



503 
471 
439 
406 
374 

342 
310 
278 
246 
214 
782" 



Log. Tan. 



Lou. Co.s 



9.95727 
9.95721 
9.95716 
9.95710 
995704 

9-95 698 
9.95692 
9.95 686 
9.95 680 
9-95 674 
9.95668 
9.95 662 

9-95656 
9.95656 

9-95644 



95638 
95632 
95627 
95621 
95615 



95609 
95603 
95 597 
95 591 
95585 
95 579 
95 573 
95 567 
95561 

95 555 



95 549 
95 543 
95 537 
95 536 
95524 



95 518 
95512 

95 506 
95 506 
95 494 



95488 
95482 

95476 
95470 
95464 



95458 
95452 
95 44? 
95 439 
95 433 



9542? 
95421 
95415 
95409 
95 403 
95 397 
95390 
95384 
95 378 
95372 

9-95 366 

Log. Sill. 





33 


6 


3-3 


7 


3-8 


8 


4.4 


9 


4-9 


10 


5-5 


20 


II. 


30 


16.5 


40 


22.0 


50 


27-5 



6 

7 
8 

9 
10 
20 
30 
40 
50 



2S 

2.6 

3-1 
3-§ 
4.0 

4-4 

8.8 

13.2 

17.6 
22.1 



32 

3 ' 
3 

4 





27 


6 


2.7 


7 


3-1 


8 


3.6 


9 


4.0 


10 


4.5 


20 


9.0 


30 


13-5 


40 


18.0 


50 


22.5 



26 

2 

3 
3 
3 
4 
8 

13 

17 
21 





8 


6 


6 


0.6 


0.6 


7 


0.7 


0.7 


8 


0.8 


0.8 


9 


I.O 


0.9 


10 


I.I 


1.0 


20 


2.T 


2.0 


30 


3-2 


3.0 ! 


40 


4-3 


4.0 


50 


5-4 


5.0 



P. V. 



64' 



53 



26^ 



TABLE IV. 



10 

II 

12 

13 

14 



15 

16 

17 
18 

20 

21 



-J 

24 

25 
26 
27 
28 
29 
30 
31 
32 
33 
34 

35 
36 
37 
38 
39 



40 

41 
42 

43 
44 

45 
46 

47 
48 

49 
50 

51 

52 
53 
54 

55 
56 
57 
58 
59 
60 



Log. Sin. 



9.64 184 
9.64 210 
9.64236 
9.64 262 
9.64 287 



9-64313 
9-64339 
9.64365 
9.64 391 
9-64416 



9.64442 
9.64468 

9-64493 
9.64519 
9.64545 



9.64 576 
9.64 596 
9.64 622 
9.6464^ 
9.64673 



9-64698 
9.64 724 

9-64749 
9.64775 
9.64 806 



9.64826 
9.64851 
9.64876 
9.64 902 
9-6492? 



9.64952 
9.64978 
9.65 003 
9.65 028 

9.65054 



9.65 079 

9.65 104 
9.65 129 

9-65 155 

9.65 180 



9.65 205 

9.65 236 
9-65255 

9.65 286 

9-65 30! 

9-65331 
9.65 356 
9.65381 

9.65 406 

9-65431 



9-65456 

9.65 481 
9.65 506 

9-65 530 
9-6555! 



9.65 580 
9.65 605 
9.65 630 

9.65655 

9.65 680 



9.65 704 



26 
26 
26 

25 

26 
26 

2S 
26 

2? 
26 
2? 
2! 
26 

2! 
2§ 
2§ 
26 

2! 
2§ 
2? 

25 
2§ 
2? 
25 
2S 
25 
25 
25 
2S 
25 
25 
25 
25 
2§ 
25 
2S 
25 
2§ 
25 
25 
2§ 
25 
25 
25 
25 
25 
25 
25 
25 
25 
25 
25 
24 

25 
25 
25 
24 
25 
25 
24 



Log. Cos. 



Log. Tan, c. d. I Log. Cot. 



9.6« 818 
9.68850 
9.68882 
9.68 914 
9-68 946 



9-68978 
9.69016 
9. 69 042 
9.69074 
9.69 106 



9.69138 
9.69 170 
9.69 202 
9.69 234 
9.69 265 
9.69 297 
9.69329 
9.69 361 

9-69393 
9.69425 



9.69456 
9.69488 
9.69 520 

9-69552 
9.69583 



9.69615 
9.69 647 
9.69678 
9.69 716 
9.69742 



9.69773 
9.69 805 
9.69837 
9.69868 
9.69 900 



9.6993! 
9.69963 
9.69994 
9.70026 
9.70058 



9.70089 
9.70 121 
9.70 152 
9.70 183 
9.70 215 



9.70246 
9.70278 
9.70309 
9.70341 
9.70372 



9.70403 

9-70435 
9.70466 
9.70497 
9.70529 



9.70 566 

9-70591 
9.70623 
9.70654 
9.70685 



9.70 716 



32 
32 
32 
32 
32 
32 
31 
32 
32 
32 
32 
32 
31 
32 
32 
31 
32 
32 
31 
32 
31 
32 

31 

32 

31 

31 

32 

31 

31 

32 

31 

31 

31 

31 

31 

31 

32 

31 

31 

31 

31 

31 

31 

31 

31 

31 

31 

31 

31 

31 

31 

31 

31 

31 

31 

31 

31 

31 

31 



0.31 182 
0.31 150 
0.31 w'j 
0.31 085 
0.31 053 



0.31 021 

0.30989 

0.3095? 
0.30 926 
0.30894 



0.30862 
0.30830 
0.30798 
o. 30 766 

0.30734 



o. 30 702 
0.30 676 

0.30639 

o. 30 607 

0.30575 



Log. Cos. 



9.95 366 
9.95 360 

9-95 353 
9-95 34? 
9-95 341 



9-95 335 
9-95 329 
9-95 323 
9-95 3'6 
9.95316 



0.30543 
0.30 511 
0.30480 
o. 30 448 
0.30 416 



o. 30 384 

030353 
0.30 321 
0.30 289 
0.30 258 

0.30226 
0.30194 
0.30 163 
0.30 1 31 
0.30 100 

o. 30 068 

0.30037 

0.30005 

0.29973 

0.29 942 



0.29 910 
0.29 879 
0.29 84^ 

0.298I6 
0.29785 



0.29753 

0.29 722 
0.29 696 
0.29 659 
0.29 628 



0.29 596 
0.29565 
0.29 533 
0.29 502 
0.29 471 



0.29439 
0.29408 
0.29377 
o. 29 346 
0.29314 



9-95 304 
9-95 298 
9.95 292 
9.95285 
9-95 279 

9-95 273 
9.95 267 
9.95 266 

9-95254 
9.95 248 



9.95242 
9-95235 
9-95 229 
9.95223 
9.95217 



9.95 210 
9.95 204 
9-95 
9-95 
9-95 



9-95 
9 95 
9-95 
9-95 
9-95 



9-95 
9-95 
9-95 
995 
9 95 



9-95 

9-95 

9-95 

9-95097 

9 95090 

9.95084 

9-95078 

9.95071 

9.95065 

9-95058 



9.95052 
9-95046 
9-95039 
9-95033 
9.95026 



0.29 283 



Log. Cot. I c. A. I Log. Tan. 



9.95 020 
9.95014 
9.95 00? 
9.95 001 
9.94994 



9-94 



Log. Sin. I 



00 

59 
58 
57 
56 



55 
54 
53 
52 
51 
oO 

49 
48 

47 
46 

45 
44 
43 
42 
41 
40 
39 
38 
37 
_3l 
35 
34 
33 
32 
31 
30 

29 
28 
27 
26 



25 
24 
23 
22 
21 



20 

19 
18 

17 
16 



15 
H 
13 
12 
1 1 

9 
8 

7 
6 



p. P. 



6 


3-2 


7 


.3.8 


8 


4-3 


9 


4-9 


10 


5-4 


20 


10.8 


30 


16.2 


40 


21.6 


50 


27.1 



6 

7 
8 

9 
10 
20 
30 
40 
50 



31 

3- J 
3-7 
4.2 

4-7 

5.2 

10.5 

15-7 
21.0 
26.2 



32 

3-2 

3-1 

4.2 

4.8 

5-3 

10.6 

16.0 

21.3 

26. § 



31 

31 

3-6 
4-1 
4.6 
5-1 
10.3 

15-5 
20.6 
25 8 





26 


2.^ 


6 


2.6 


2.5 


7 


3-0 


3-0 


8 


3-4 


3-4 


9 


3-9 


3-8 


10 


4-3 


4.2 


20 


8.6 


8.5 


30 


13.0 


12.? 


40 


17-3 


17.0 


50 


21.6 


21.2 



24 



6 

7 
8 

9 
10 
20 
30 
40 
50 



2.4 


0.6 


2.8 
3-2 


0.7 
0-8' 


3-7 


I.O 


4.1 
8.1 


I.I 

2.T 


12.2 


3.2 


16.3 


4-3 


20.4 


5-4 



25 

2.5 

2-9 

3-3 
3-? 
4.1 

8.3 
12.5 

16.6 
20.8 



8 6 

1 0.6 
jo.7 
0.8 

0-9 
1.0 
2.0 
30 
4.0 
5.0 



63' 



54 



TABLE IV. 



27 



5 
6 

7 
8 

9 

10 

II 

12 

13 

i£ 

i6 

17 

i8 

19 



20 

21 
22 

23 
_2£ 

25 
26 

27 
28 

29 

30 

31 
32 
33 
34 

35 
36 
37 
38 
39 



40 

41 

42 

43 
44 



45 
46 

47 
48 

49 

60 

51 
52 
53 
54 

55 
56 
57 
58 
59 
60 



Log. Sill. 

9-65 704 
9.65 729 
965754 
9.65 779 
9.65 803 



9-65828 

9-65853 
9.65 878 

9.65 902 

9-65927 

9.65951 

9-65 976 
9.66001 

9.66025 

9.66 050 



9.66 074 
9. 66 099 
9.66 123 
9.66 148 
9.66 172 



9.66 197 
9.66 221 
9.66 246 
9.66 276 
9.66 294 



9. 66 3 1 9 
9-66 343 
9.66 367 
9.66 392 
9-66 416 



9.66 440 
9.66465 
9.66 489 
9-66513 
9-66 537 



9.66 561 
9.66 586 
9.66610 
9.66 634 
9.66658 



9.66682 

9-66 706 
9.66 730 

9-66754 
9-66 778 



9.6680: 
9.66 82g 
9.66 856 
9.66874 
9-66 898 
9.66 922 
9.66946 

9.66 976 
9.66994 

9.67 018 



9.67 042 
9.67 066 
9.67 089 
9.67 113 
9-67 137 
9.67 161 

Log. Cos. 



25 
^i 
25 
24 

25 

24 

25 
24 

24 
24 
25 
24 
24 
24 
24 
24 
24 

24 
24 

24 

24 

24 
24 

24 
24 
24 
24 
24 

24 
24 
2-1 
24 
24 
24 

24 
24 

24 
24 
24 

24 
24 
24 
24 
24 
24 
24 
24 
24 
24 
24 
24 
24 

23 
24 

24 
24 

23 
24 
23 

24 



Lojr. Tail. c. d 



70 7 16 
70748 
70779 
70810 
70841 



70872 
70903 

70935 
70 966 
70997 



028 
059 
090 
121 
152 



183 
214 

24§ 
276 
307 



338 
369 
400 

43'' 
462 



493 

524 

555 
586 
617 



647 
678 
709 
740 

771 



801 
832 
863 
894 
925 



7195? 

7 

72 017 

72047 

72078 



72 109 
72 139 
72 170 
72 201 
72 231 



72 262 

72 2Q2 
72 323 
72354 
72384 



72415 

72445 
72476 
725O6 
72537 
72 567 



Log. Cot. c. (1 



3' 
3' 
31 
31 
31 
31 
3' 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 



31 
30 
31 
31 
31 
30 
31 
31 
30 
31 
30 
31 
31 
30 
31 
30 
30 
31 
30 
31 
30 
30 
30 
31 
30 

30 
30 
30 
31 
30 
30 
30 
30 
30 
30 
30 



Log. Cot. 
0.29 283 
0.29 252 
0.29 221 
0.29 190 

0.29 158 



0.29 127 
o. 29 096 
0.29065 
0.29034 
o. 29 003 



0.28 972 
o. 28 946 
o. 28 909 

0.28 878 
0.2884^ 



0.28 816 
0.28 78| 
0.28754 
0.28 723 
0.28 692 



0.28 661 
0.28 636 
0.28 599 
0.28 568 
0.28537 



o. 28 505 
0.28 476 
0.28445 
0.28 414 
0.28383 



0.28352 
0.28 321 
0.28 290 
o. 28 260 
0.28 229 



0.28 198 

0.28 167 

0.28 136 
0.28 106 
0.28 075 



o. 28 044 
0.28 014 
0.27983 
0.27 952 
0.27 921 



0.27 891 
0.27 860 
0.27 830 
0.27799 
0.27768 



0.27738 
0.27 707 
0.27 677 
0.27 646 
0.27 615 



0.27 585 

0.27 554 
0.27 524 

0-27493 
0.27463 

0-27432 

Log. Tan. 



Log. Cos. 
94988 
94981 

94 975 
94969 
94962 



94 956 
94 949 
94 943 
94 936 
94930 



94923 
94917 
94916 
94904 
94897 



94891 
94884 
94878 
94871 
94865 



94858 
94852 
94845 

94839 
94832 



94825 
94819 
94 812 
94 806 
94 799 
94 793 
94786 
94 779 
94 773 
94766 



94760 
94 753 
94 746 
94740 

94 733 



94727 
94726 

94713 
94707 
94706 




94627 
94 626 
94613 
94607 
94 600 

9-94 593 



Log. Sill. 



(>0 

59 
58 

57 

55 
54 
53 
52 
51 
60 

49 
48 

47 
46 



45 
44 
43 
42 

41 
40 

39 
38 
37 
36 



35 
34 
33 
32 
31 
30 

29 
28 

27 
26 



25 
24 

23 
22 
21 

"20 

19 

18 

17 
16 



15 
14 
13 
12 
II 

To 

9 
8 

7 
6 



P. P. 



6 

7 
8 

9 
10 

20 
30 
40 
50 



31 

3-1 
3-7 
4.2 
4-7 
5-2 
10.5 

I5-? 
21.0 
26.2 



31 

3-1 
3-6 
4.1 

4-6 

5-1 

10.3 

15-5 
20.6 
25-8 





25 


6 


2.5 


7 


2.9 


8 


3.3 


9 


3-7 


10 


4.1 


20 


8., 3 


30 


12.5 


40 


16-6 


50 


20.8 





24 


24 


23 


6 


2.4 


2.4 


2. 


7 


2.8 


2.8 


2. 


8 


3-2 


3-2 


3- 


9 


' 3-7 


3.6 


3- 


10 


4.1 


4.0 


3- 


20 


8.T 


8.0 


7- 


30 


12.2 


12.0 


II. 


40 


16.3 


16.0 


15- 


50 


20.4 


20.0 


19- 





7 


§ 


6 


0.7 


0.6 


7 


0.8 


0.7 


8 


0.9 


0.8 


9 


I.O 


1.0 


10 


i.i 


I.I 


20 


2.. 3 


2.1 


30 


3-5 


3-2 


40 


4-6 


4-3 


50 


5-8 


5-4 



62^ 



55 



28^ 



TABLE IV. 



Lo!?. Sin. 



9.67 161 
9.67 184 
9.67 208 
9.67 232 
9.67 256 



10 

II 

12 

14 



15 
16 

18 
19 



20 

21 

22 

23 
24 



25 
26 
27 
28 
29 



30 

31 
32 
33 
34 



35 

36 
37 
38 
39 



40 

41 

42 
43 
44 

45 
46 

47 
48 

49 
50 

51 

52 
53 
54 



55 
56 
57 
58 
59 



60 



9.67279 
9.67 303 
9.67327 
9.67 350 
9-67 374 



9.67 39? 
9.67 421 
9.67445 
9.67468 
9.67492 



9.67515 

9-67 539 
9.67 562 
9.67 586 
9.67 609 



9-67633 
9.67 656 
9.67679 
9.67703 
9.67726 



9.67 750 
9.67773 
9-67 796 
9.67 819 
9.67843 



9.67 866 
9.67 889 
9.67913 
9.67936 
9.67959 



9.67 982 

9.68 005 
9.68 029 
9.68052 
9.68075 



9.68 098 
9.68 121 
9.68 144 
9.68 16^ 
9.68 190 



9.68 213 
9.68236 
9.68 259 
9.68282 
9.68 3o§ 



9.68 328 
9.68351 
9.68374 
9.68 397 
9.68 420 



9.68443 
9.68466 
9.68488 
9.68 511 
9.68 534 



9-68557 

Log. Co.s. d 



23 

24 

23 

24 

23 
23 
24 
23 
23 

23 

24 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

23 

22 

23 
23 
23 

22 

23 

23 

22 



Lof?. Tan. 



9.72567 
9.72 598 
9.72628 
9.72659 
9.72 689 



9.72719 
9.72750 
9.72 780 
9.72 811 
9.72841 



9.72 871 
9.72 902 
9.72932 
9.72 962 
9.72993 



9-73023 

9-73053 
9.73 0S4 

9-73 114 
9-73 144 



9-73 174 
9.73205 

9-73235 
9.73265 

9-73295 



9-7332! 
9-73356 
9-73386 
9.73416 
9-73 446 



9-73 476 
9-73 506 
9-73 536 
9-73567 
9-73 597 



9.73627 

9-73657 
9.73687 

9-73717 
9-73 747 



9-73 777 
9.73807 

9-73837 
9.73867 

9-73897 



9.73927 
9.73957 
9-73987 
9.74017 
9.74047 



9- 74076 
9.74 log 

9-74136 
9.74 166 
9.74 196 



c. d. I Log. Cot. Locr. Cos 



9.74 226 
9-74256 
9.74286 
9-74315 

9-74 34g 

9-74 375 

Log, Cot. c. d 



30 
30 
30 
30 

30 
30 
30 
30 
30 
30 
30 
30 
30 
30 

30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 

30 
30 
30 
30 
30 
29 
30 
30 
30 
29 
30 
30 
30 
29 
30 
29 



0.27432 
0.27 402 
0.27371 
0.27341 
0.27 31 1 




0.26976 
0.26946 
0.26916 
0.26886 
0.26855 



0.26 825 
0.26 795 
0.26 765 
0.26734 
o. 26 704 



o. 26 674 
o. 26 644 
0.26 614 
0.26 584 

0.26553 



9-94 593 
9.94587 
9.94580 
9-94 573 
9.94566 



9.94560 
9-94 553 
9-94 546 
9-94 539 
9-94 533 



9.94 526 
9.94519 
9.94512 
9.94 506 
9-94 499 



9.94492 
9.94485 

9-94 478 
9-94472 
9.94465 



9.94458 
9.94451 
9-94 444 
9-94 43? 
9-94431 



0.26 523 
0.26493 
0.26463 
0.26433 
o. 26 403 



0.26373 
0.26343 
0.26313 
0.26 283 
0.26 253 



0.26 223 
0.26 193 
0.26 163 
0.26 133 
0.26 103 



0.26073 
o. 26 043 
0.26013 
0.25 983 

0-25953 



0.25 923 
0.25 893 
0.25 863 

0.25833 

0.25 804 



0.25774 
0.25744 
0.25714 

0.25 684 

0.25654 

0.25 625 
Log. Tan. 



9.94424 
9.94417 
9.94410 
9-94403 
9-94 396 



9-94390 
9-94383 
9-94376 

9-94369 
9.94 362 



9-94 35S 
9-94 348 
9-94 341 
9.94335 
9-94328 



9.94321 
9-94314 
9-94 307 
9-94300 
9-94 295 



9.94286 
9.94 279 
9-94272 
9-94265 

9-9 4 2 58 
9-94251 
9-94245 
9-94238 
9-94231 
9.94224 



9-94217 
9.94 210 
9.94203 
9.94196 
9-94 189 
9.94 182 

Log. Sin. 



GO 

59 
58 

57 

55 
54 
53 
52 
51 
60 
49 
48 
47 
46 

45 
44 
43 
42 
41 
40 
39 
38 
37 
_3i 
35 
34 
33 
32 
31 
30 

29 
28 
27 
26 



25 
24 
23 
22 
21 

"20 

19 
18 

17 
16 



15 
14 
13 
12 
II 

To 

9 

8 

7 
6 

5 
4 
3 
2 
I 

~0" 





30 


30 


6 


3-6 


3-0 


7 


3-5 


3-5 


8 


4.0 


4.0 


9 


4.6 


4-5 


10 


5-1 


5.0 


20 


10. 1 


lO.O 


30 


15.2 


15.0 


40 


20.3 


20.0 


50 


25.4 


25.0 



6 

7 
8 

9 
10 

20 

30 
40 

50 



24 

2.4 

2.8 

3-2 

3-6 

4.0 

8.0 

12.0 

16.0 

20.0 



29 

2-9 

3-4 

3-9 

4-4 

4-9 

9-8 

14-? 

19-6 

24.6 





23 


23 


6 


2-3 


2.3 


7 


2.7 


2.7 


8 


3-1 


3-0 


9 


3-5 


3-4 


10 


3-9 


3-8 


20 


7-8 


7-6 


30 


II. 7 


II. 5 


40 


15-6 


15-3 


50 


19.6 


19.1 



22 

2.2 
2.6 
3-0 

3-4 

7-5 
II. 2 
15.0 
18.; 



6 

7 
8 

9 
10 
20 
30 
40 
50 



7 

0.7 
0.8 
0.9 

I.O 

I.I 

2.3 

3-5 
4-6 
5-8 



o.§ 
0.1 

0.8 
1.0 
I.I 
2.1 
3-2 
4-3 
5-4 



P. P. 



61 



56 



TABLE IV. 



29^ 



10 

II 

12 

14 



15 
i6 

i8 
19 



20 

21 

22 

23 
24 



25 
26 

27 
28 



30 

31 

32 

33 

34 



35 
36 
37 
38 
39 



40 

41 
42 

43 
44 

45 
46 

47 
48 

49 



50 

51 
52 
53 

54 

55 
56 
57 
58 
59 
(50 



9.68 557 
9.68 580 
9. 68 602 
9.68625 
9.68 648 
9y6S"67i 
9.68 693 
9.68 716 
9.68739 
9.68 761 



9.68 784 
9.68 807 
9.68 829 
9.68852 
9. 68 874 



9.68 897 
9.68 920 
9.68 942 
9.68 965 
9.68 987 



9.69 010 
9.69032 
9.69055 
9.69077 
9.69099 



9.69 122 
9.69 144 
9.69 167 
9.69 189 
9.69 21 T 



9.69 234 
9.69 256 
9.69278 
9.69 301 
9.69323 



9-6934? 
9.69 367 
9.69390 
9.69 4r2 
9-69434 



9-69 456 
9-69 478 
9.69 500 
9.69 523 
9.69 545 



9.69 567 
9.69 589 
9.69 611 
9.69633 
9-6965? 



9.69677 
9.69699 
9.69 721 
9-69743 
9-6 9 76g 
9.69 78f 
9.69 809 
9.69 831 
9.69853 
9.69875 



9- 69 897 
Loe. Cos. 



23 



23 



22 
22 



22 
22 
22 
21 

22 
22 



l.oi.'. Tiui. 

9-74 375 
9.74405 

9-74 435 
9- 74 464 
9-74 49-1 



9.74524 
9.74554 
9-74583 
9.74613 

9- 74 643 



9.74672 
9.74702 
9-74 732 
9.74761 

9-74 791 
9.74821 
9.74850 
9.74 880 
9.74909 
9-74 939 



9.74969 

9-74 998 
9.75028 
9.7505^ 
9.75087 



9-75 I '6 
9.75 146 

9-75 I7§ 
9.75 205 

9-75234 



30 

30 
29 

30 
29 
30 
29 
29 
30 
29 
30 
29 
29 
30 
29 

29 
29 
29 
30 

29 
29 
29 
29 
29 
29 

29 
29 

29 
29 

29 
29 
29 
29 
29 

29 
29 

29 
29 
29 
29 
29 
29 
29 

29 

29 
29 

29 
29 
29 
29 
29 
29 
29 
29 

29 
29 
29 
29 
29 
29 
Log. Co t, c. (1. 



9.75 264 

9-75 293 
9-75323 
9-75352 
9.75382 



9.75 411 

9-75 441 
9.75470 

9-75 499 
9.75 529 



9-75 558 
9.75 588 
9.75617 

9.75646 
9.75676 



9-75705 

9-75 734 
9.75764 

9-75 793 
9.75 822 



9.75851 
9.75881 
9.75910 
9-75 939 
9.75968 



9.75998 
9.76 027 
9.76056 
9.7608? 
9-76 115 
9.76 144 



0.25625 
0.25 595 
0.25 565 
025 535 
0.25505 



0.25 476 
0.25446 
0.25 416 
0.25 387 

0-25 357 
0.25 32^ 
0.25 297 
0.25 268 
0.25 23g 
0.25 208 



l.iiif. Cds. 
9.94 182 
9.94 175 
9.94 168 
9.94 161 

9-94 154 



0.25 179 
0.25 149 
0.25 120 
0.25 090 
o. 2 5 060 



0.25 031 
0.25 001 
0.24 972 
0.24 942 
0.24913 



0.24 883 
0.24854 
0.24824 
0.24795 
0.24 765 
0.24 736 
0.24 706 
0.24677 
0.2464^ 
o. 24 6 1 8 



0-24588 
0.24559 
0.24 529 
o. 24 506 
0.24471 



0.24441 
0.24 412 
0.24383 
0.24353 
0.24324 



0.24 295 
0.24 26? 
0.24 236 
o. 24 207 
0.24 17^ 



0.24148 

0.24 119 
o. 24 090 
o. 24 060 
0.24031 



0.24002 

0.23973 
0.23943 
0.23914 
0.23885 



0-23856 

Log. Tnii. 



9 94 147 
9.94 140 

9-94133 
9.94 126 

9-94 11 8 
9.94 III 
9.94 104 
9.94097 
9.94096 
9.94083 



9-94 076 
9.94069 
9.94062 
9.94055 
9.94048 



9.94041 
9.94034 
9.94025 
9.94019 
9.94012 



9.94005 
9.93998 
9-93 991 
9-93984 
993 977 
9.93 969 
9.93 962 

9-93 95? 
9-93948 
9-93 941 



9-93 934 
9.93 926 
993919 
9.93912 

9-93 905 



9.93898 

9-93 891 
9-93883 
9-93876 
9-93 869 
9.93 862 
9-93854 
9-93 84^ 
9.93840 

9-93833 



9.93 826 

9-93 818 
9-93811 
9.93 804 

9-93 796 



993789 
9.93782 

9-93 775 
9.9376? 
9.93766 



9-93 753 

Log. JSin. 



(iO 

59 
58 
57 

55 
54 
53 
52 
J[ 
50 
49 
48 
47 

45 
44 
43 
42 

41 
40 

39 

38 

37 

J6_ 

35 
34 
33 
32 
31 
30 

29 
28 

27 
26 



25 
24 

23 
22 
21 

"20" 

19 
18 

17 
16 

14 
13 
12 
II 
~w 
9 

8 

7 
6 



6 

7 
8 

9 
10 
20 
30 
40 
50 



30 

3.0 

3-5 
4.0 

4.5 
5.0 
lo.o 
15.0 
20.0 
25.0 



29 

2.9 
3-4 
3-9 
4-4 
4.9 

9.8 
14. f 
19-6 
24.6 





23 


6 


2-3 


7 


2.7 


8 


3-0 


9 


3-4 


10 


3-8 


20 


7.S 


30 


II. 5 


40 


15-3 


50 


1 9. 1 



29 

2.9 

3-4 
3-8 
4-3 
4-8 
9-6 
14.5 

19.3 
24.1 





22 


22 


6 


2.2 


2.2 


7 


2.6 


2.? 


8 


3.0 


2.9 


9 


3.4 


3-3 


10 


3-7 


3-6 


20 


7.5 


7.3 


30 


II. 2 


II. 


40 


15.0 


14.6 


50 


m.f 


18.3 



21 

2.1 
2.5 
2.8 

3.2 

3-6 
7.1 

lO.f 

14-3 
17.9 



6 


0.7 


7 
8 


0.9 

I.O 


9 
10 


I.I 
1.2 


20 


2-5 


30 
40 
50 


3-f 
5.0 
6.2 



7 

0.7 
0.8 
0.9 
1.0 
I.I 
2-3 
3-5 
4-6 
5.8 



p. P. 



60^ 



57 



30^ 



TABLE IV. 



10 

II 

12 

13 

14 



20 

21 

22 
23 

24 



25 
26 
27 
28 
29 



30 

31 

32 

33 

34 

35 
36 
37 
38 
39 



40 

41 
42 

43 
44 



45 
46 

47 
48 

49 
50 

51 
52 

53 
54 



55 
56 
57 
58 
59 



GO 



Log. Sin. 
9.69897 
9.69919 
9.69946 
9.69 962 
9.69984 



9.70006 
9.70028 
9.70050 
9.70071 
9.70093 



9-70115 
9.70 137 

9.70158 
9.70 180 
9.70 202 



9.70 223 
9.70245 
9.70 267 
9.70288 
9.70310 



9-70331 
9-70353 
9-70375 

9- 70 396 
9.70418 



9-70439 
9.70461 
9.70482 
9.70504 
9.70525 



9-70547 
9.70568 
9.70 590 
9.70 61 1 
9.70632 



9.70654 
9.70675 
9.70696 
9.70718 
9.70739 



9.70 766 
9.70782 
9.70803 
9.70 824 
9. 70 846 



9.70867 
9.70888 
9.70909 
9.70930 
9-70952 

9-70973 
9-70994 
9.71 015 

9-71 036 
9.71 057 



9.71078 
9.71 099 
9.71 121 
9.71 142 
9.71 163 



9-71 184 

Log. Cos. 



2? 



21 
22 
21 
21 
22 
21 
21 
22 
21 
21 
21 
22 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 



Log. Tan. 

9.76 144 
9.76 173 
9.76 202 
9.76231 
9.76 266 



9.76 289 
9.76319 
9.76348 

9-7(>2>77 
9.76406 



9- 76 435 
9.76464 

9-76493 
9.76 522 

976551 
9.76 586 
9.76 609 
9.76638 
9.76667 
9. 76 696 



9.76725 
9.76754 

9-76783 
9.76 812 
9.76 841 



9.76 870 
9.76899 
9.76 928 
9.76957 
9.76 986 



9-77015 
977043 
9.77072 
9.77 lOI 
9-77 130 



9-77 159 
9.77188 
9.77217 
9.77245 

9-77274 



9-77303 
9-77332 
9.77361 

9-77 389 
9-77 418 



9-77 447 
9.77476 

9-77 504 
9-77 533 
9.77 562 



9-77 591 
9.77619 
9.77648 
9.77677 
9.77705 



9-77 734 
9-77763 
9.77791 
9.77 820 
9-77 849 
9-7787^ 
Log. Cot. 



c. d. I Log. Cot. 



29 
29 
29 

29 
29 

29 
29 

29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 

29 
29 
29 

29 
29 

29 
28 

29 
29 
29 

29 

28 

29 
29 
29 

28 

29 
29 

28 

29 
29 

28 

29 

28 

29 

28 

29 

28 

29 

28 

29 



29 

28 
28 

29 

28 
28 

29 

28 



0.23856 

0.23 827 

0.2379? 
0.23768 
0.23739 



0.23 710 
0.23 681 
0.23 652 
0.23 623 
0-23 594 
0.23565 

0-23 53? 
0.23 506 
0.23477 
0.23 448 



0.23419 
0.23396 
0.23361 
0.23332 
0.23303 



0.23 274 
0.23245 

0.23 216 

0.23 i8f 
0.23 158 
0.23 129 
0.23 lOI 
0.23 072 
0.23043 
0.23 014 



0.22 985 
0.22 956 
0.22 927 
0.22 898 
0.22 86q 



0.22 841 
0.22 812 
0.22 783 

0.22754 

0.22 725 



0.22 696 

0.22668 

0.22 639 
0.22 616 
0.22 581 



0.22553 

0.22 524 
0.22 495 
0.22 466 
0.22 438 



0.22 409 
0.22 380 
0.22 352 
0.22 323 
0.22 294 



0.22 266 
0.22 237 
0.22 208 
0.22 180 
0.22 151 



o. : 



12: 



Log. Tan. 



Log. Cos. 



9-93 753 
9-93746 
9-93 738 
9-93731 
9-93724 



9-93 716 
9.93709 

9-93 702 
993694 
9.93687 



9.93 680 
9-93672 
9-93665 
9.93658 
9.93656 



9-93643 
9-93635 
9-93628 
9.93 621 

9-93613 



9.93 606 
9-93 599 
9-93 591 
993584 
9-93 576 



9-93 569 
9.93 562 

9-93 554 
9-93 547 
9-93 539 



993532 
9-93 524 
9-93517 
9-93 509 
9-93 502 



9-93 495 
9-9348? 
9.93480 
9-93472 
9-93465 



9-93 457 
9-93450 
9-93 442 
9-93 435 
993427 



9.93420 
9.93412 
9-93405 
9-93 39? 
9-93390 



9-93 3S2 
9-93 374 
9-93367 
9-93 359 
9-93 352 



9-93 344 
9-93 337 
9-93 329 
9-93321 
9-93314 



9-93 306 

Log. Sin. 



45 
44 
43 
42 
41 
40 
39 
38 
37 
36 



35 
34 
33 
32 
31 
30 

29 
28 
27 
26 



25 
24 



21 
"20 

19 



18 

17 
16 



15 
14 
13 
12 
II 

To 

9 

8 

7 
6 



p. p. 





29 


29 


6 


2-9 


2.9 


7 


3-4 


3-4 


8 


3-9 


3-8 


9 


4-4 


4-3 


10 


4-9 


4-8 


20 


9-8 


9-6 


30 


147 


14.5 


40 


19-6 


19-3 


50 


24.6 


24.1 





8 


1 


6 


0.8 


o.f 


7 
8 


0.9 
1.6 


0.9 

I.O 


9 
10 


1.2 
I. .3 


I.I 

1.2 


20 


2-6 


2-5 


30 


4.0 


3-7 


40 
50 


5.3 
6.6 


5.0 
6.2 



p. p. 



28 

2-8 

3-3 

3-8 

4-3 

4-? 

9-5 

14.2 

19.0 

23.? 





22 


21 


6 





2.1 


7 
8 


2-5 
2.9 


2.5 

2-8 


9 


3-3 


3-2 


10 


3-6 


3-6 


20 


7-3 


7-1 


30 


II. 


10.7 


40 


14-6 


14-3 


50 


18.3 


17.9 



21 

2.1 

2-4 
2.8 

3-1 

3-5 

7.0 

10.5 

14.0 



7 

0.7 
0.8 
0.9 
1.6 
I.I 
2-3 
3-5 
4-6 
5-8 



59' 



58 



TABLE IV. 



31 



hoft. Sill. 



10 

I II 

12 

13 
14 

15 
i6 

17 
i8 

19 



20 

21 
22 
23 
24 

25 
26 

27 
28 
29 



30 

31 

32 
33 

34 

35 

36 
37 
38 
39 



40 

41 

42 
43 
44 

45 
46 

47 
48 

49 



50 

5' 

52 
53 
54 

55 
56 
57 
58 

GO 



184 
205 
226 

247 
268 



289 
310 
331 
351 
372 



393 
414 

435 
456 

477 



498 
5'8 
539 
560 

581 



601 
622 

643 
664 
684 



70S 
726 

746 
76? 
788 



808 
829 

849 
876 
891 



911 
932 
952 
973 
993 



72 014 
72034 
72055 
72075 
72 096 



72 1 16 
72 136 
72 157 
72 177 
72 198 



72 218 
72 238 
72259 
72279 
72 299 



72319 
72340 
72 366 
72386 
72 406 
9.72 421 

Log. Cos. 



21 
21 
21 
21 
21 
21 
21 
20 
21 
21 
21 
26 
21 
21 
21 
26 
21 
26 
21 
26 
21 
20 
21 
26 
21 
26 
26 
21 
20 
26 
20 
26 
21 
20 
20 
20 
20 
20 
20 
26 
20 
26 
26 
26 
20 
20 
26 
20 
26 
20 
26 
26 
20 
20 
20 
26 
26 
20 
20 
26 



Lop. Tan. 




163 
191 
220 

248 
277 



30S 
334 
362 

391 
419 



448 
476 
505 
533 
561 



590 
618 
647 
675 
703 



732 
760 

788 
817 

845 



873 
902 

930 
958 
987 



015 

043 
071 
100 
128 



156 
184 

213 
241 
269 

29^ 
32§ 
354 
382 
410 



438 
466 
494 
522 

551 



79 579 
Log. Cot. 



c (1. I Loir. Cot. 



28 
28 
28 

29 

28 
28 
28 
28 
28 
28 
28 
28 
28 
28 
28 
28 
28 
28 
28 



28 



28 

28 



28 

28 

28 

28 

28 
28 

28 

28 

28 

28 

28 

28 

28 

28 

28 
28 

28 

28 



28 



28 



C. (1. 



0.22 122 

0.22 094 
0.22 065 

0.22037 

0.22 008 



0.2 
0.2 
0.2 
0.2 
0.2 



0.2 
0.2 
0.2 
0.2 
0.2 



0.2 
0.2 
0.2 
0.2 
0.2 



0.2 
0.2 
0.2 
0.2 
0.2 



0.2 
0.2 
0.2 
0.2 
0.2 



0.2 
0.2 
0.2 
0.2 
0.2 



0.2 
0.2 
0.2 
0.2 
0.2 



979 
95" 

Q22 

894 
865 



837 
808 

780 

751 
723 



694 

666 

63? 

609 

586 



552 
523 

495 

467 

438 



410 

38r 

353 
325 

296 



268 

239 
211 

183 

154 



126 

098 
070 
041 
013 



0.20 985 
0.20 956 
0.20 928 
o. 20 900 
0.20 872 



0.20 843 
0.20 81 § 
0.20787 
0.20 759 
0.20 731 



0.20 702 
0.20674 
o. 20 646 
o. 20 6 1 8 
0.20 590 



0.20 561 
0.20533 
0.20 50^ 
0.20 47 f 
o. 20 449 
0.20421 

Log. Tan. 



(iif. Cos. 
93 306 
93 299 
93291 
93284 
93276 



93268 
93261 
93253 
93245 
93238 



93230 
93223 

93215 
93207 
93 200 



93 192 
93 184 
93 ^77 
93 169 
93 161 



93 153 
93 '46 
93 138 
93 136 
93 123 



93 115 
93 10^ 
93 100 
93 092 
93084 



93076 
93069 
93 061 
93053 
93045 



93038 
93030 
93 022 

93014 
93006 



92999 
92991 
92983 

92975 
92 967 



92 960 

92952 
92944 

92936 
92928 



92 920 
92913 

92905 
92897 
92889 




Log. Sin. 



(JO 

59 
58 
57 
56 



55 
54 
53 
52 
5' 
50 

49 
48 

47 

45 
44 
43 
42 
41 
40 
39 
38 
37 
36 



35 
34 
33 
32 
31 
30 
29 
28 

27 
26 



25 

24 

23 
22 
21 

"20 

19 

18 

17 
16 



15 

14 
13 
12 
1 1 

To 

9 

8 

7 
6 



V. p. 





.29 


28 


6 


2.9 


2-8 


7 


,3-4 


3-3 


8 


3-8 


3-8 


9 


4-3 


4-3 


10 


4-8 


4-7 


20 


9-6 


9-5 


30 


14.5 


14.2 


40 


19-3 


19.0 


50 


24.1 


23.7 



28 

2.8 

3-2 

3-? 

4.2 

4-6 

9-3 

14.0 

i8.§ 

23-3 





21 


20 


6 


2.1 


2.6 


7 


2.4 


2.4 


8 


2.8 


2.7 


9 


3.1 


3-1 


10 


.3-5 


.3-4 


20 


7.0 


6.8 


30 


10.5 


10.2 


40 


14.0 


13-6 


50 


17-5 


17.1 



20 

2.0 

2-3 
2.6 

30 

3-3 
6.6 

lO.O 

13-3 
16.6 



6 

7 
8 

9 
10 
20 
30 
40 
50 



8 

0.8 
0.9 
1.6 
1.2 
1-3 
2.6 
4.0 

5-3 
6.6 



1 

0.1 
0.9 
i.o 
I.I 
1.2 
2.5 
3-f 
5.0 
6.2 



P. P. 



58^ 



59 



32° 



TABLE IV. 





I 

2 

3 

4 

5 
6 

7 
8 

9 
10 

II 

12 

13 
14 



15 

i6 

17 
i8 

19 



20 

21 
22 
23 
24 

25 
26 

27 
28 

29 

30 

31 
32 
33 
34 

35 
36 
37 
38 
39 



40 

41 
42 
43 
44 



45 
46 

47 
48 

49 
50 

51 

52 
53 

54 



55 
56 
57 
58 
59 
60 



Log. Sin. 

9.72 421 
9.72441 
9.72461 
9.72481 
9.72 501 



9.72 522 
9.72 542 
9.72 562 
9.72 582 
9.72 602 



9.72 622 
9.72 642 
9.72 662 
9.72682 
9.72 702 



9.72723 

9-72 743 
9.72763 
9.72783 
9.72 802 



9.72 822 
9.72 842 
9.72 862 
9.72882 
9.72 902 



9.72 922 
9.72942 
9.72 962 
9.72 982 
9.73002 



9.73 021 
9.73041 
9.73 061 
9.73081 
9.73 lOI 



9.73 120 
9.73 140 
9.73 160 
9.73 180 
9-73 199 



73219 
73239 
73258 
73278 
73298 



7331^ 
73 33? 
73 357 
73 376 
73396 



73 4i§ 
7343S 
73 455 
73 474 
73 494 



9-73 513 
9-73 533 
9-73552 
9-73 572 
9-73 591 
9-73611 

_Log. Cos^ 



20 
26 
20 
20 
20 
20 
20 
20 
20 
20 
20 
20 
20 
20 
20 
20 
20 
20 
19 
20 
20 
20 
20 
20 
20 

19 
20 
20 

20 

19 

20 
20 

19 
20 

19 
20 

19 
20 

19 
20 

19 
19 
20 

19 

19 

20 

19 
19 
19 

19 

20 

19 
19 
19 
19 
19 
19 
19 
19 
19 



Log. Tan. v. d 



9-79 
9-79 
9-79 
9-79 
979 
9-79 
9-79 
9-79 
9-79 
9-79 



579 
607 

635 
663 
691 
7T§ 
747 
77l 
803 

83J 



9-79 
9-79 
9-79 
9-79 
9-79 



9-79 
9.80 
9.80 
9.80 
9.80 



859 
887 
915 
943 
971 

999 
027 

055 
083 
I II 



9.80 
9.80 
9.80 
9.80 
9.80 



139 
16^ 

19? 
223 
251 



9.80 
9.80 
9.80 
9.80 
9.80 



279 
307 
335 
363 
391 



9.80 
9.80 
9.80 
9.80 
9.80 



418 
446 
474 
502 

530 



28 
28 
28 
28 
28 
28 
28 
27 
28 
28 
28 
28 

2f 
28 

28 
28 
2f 
28 
28 
2f 
28 
28 

2? 
28 
2? 
28 
28 
27 
28 
2f 
28 
27 
28 
2f 
27 
28 
2f 
28 

2? 
2f 
28 
27 

Log. Cot . I c . d . 



9.80 
9.80 
9.80 
9.80 
9.80 



558 

586 
613 
641 
669 



9.80 
9.80 
9.80 
9.80 
9.80 



697 
725 
752 
780 



9.80 
9.80 
9.80 
9.80 
9.80 



836 
864 
89T 
919 
947 



9.80 
9.81 
9.81 
9.81 
9.81 



975 
002 
030 
058 
08? 



9.81 
9.81 
9.81 
9.81 

9.81 

9.81 251 



113 
141 
168 

196 

224 



28 
28 
28 
28 
28 
28 
28 
28 
28 
28 



28 



28 



Log. Cot. 
0.20421 
0.20393 
0.20 365 
0.20337 
0.20 3O8 



0.20 286 
0.20 252 
0.20 224 
0.20 196 
0.20 168 



0.20 140 
0.20 112 

o. 20 084 

0.20055 
0.20 028 



o. 20 000 

O. 

o. 
o. 
o. 



9972 

9 944 
9916 

9888 



9 866 
9832 
9 804 
9 776 
9 748 



9721 

9693 
9665 

9637 
9609 



9581 

9 553 
9 52§ 

9 49? 
9470 



9442 
9414 

9386 
9 358 
9336 



9303 
9275 
924? 
9219 
9 191 



9164 
9136 

9 108 
9 086 

9053 



9025 

8997 
8970 
8942 
8914 



8 886 
8859 
883T 
8803 

8 776 

0-18748 

Log. Tan. 



Log. Cos. 
9.92 842 
9.92834 
9.92825 
9.92 8I8 
9.92 816 



9.92 802 
9.92794 
9.92785 

9-92 778 
9.92771 



9.92 763 

9-92755 
9.92 747 
9.92739 
9.92731 



9.92723 
9.92715 
9.92 707 
9.92699 
9.92 691 



9.92 683 
9.92675 
9.92 667 
9.92659 
9.92 651 



9.92643 
9-92635 
9.92 627 
9.92619 
9.92611 



9.92 603 
9-92 595 
9-92 587 
9-92 579 
9.92 576 



9.92 562 
9.92 554 
9-92 546 
9-92 538 
9.92 536 



9.92 522 
9.92514 
9.92 506 
9.92498 
9.92 489 



9.92 481 

9-92473 
9.92 46§ 

9-92457 
9-92449 



9.92441 

9-92433 
9.92424 
9.92415 
9.92 408 



9.92 400 
9-92 392 
9-92383 
9-92 37§ 
9-92 36? 

9-92359 

Log. Sin. 



00 

59 
58 
57 

jl 

55 
54 
53 
52 
51 
oO 

49 
48 

47 
_46_ 

45 
44 
43 
42 

41 
40 

39 
38 
37 
_3i 
35 
34 
33 
32 
31 
30 
29 
28 

27 
26 

25 
24 

23 

22 
21 

"20 

19 
18 

17 
16 

15 
14 
13 
12 
II 

lo 

9 
8 

7 
6 



p. P. 





28 


28 


2? 


6 


2.8 


2.8 


2.7 


7 


3-3 


.3-2 


,3-2 


8 


3-8 


3-y 


3-6 


9 


4-3 


4-2 


4-1 


10 


4-7 


4-6 


4-6 


20 


9-5 


9-3 


9-1 


30 


14.2 


14.0 


13.7 


40 


19.0 


18.6 


18.3 


50 


23-7 


23-3 


22.9 





20 


20 


6 


2.6 


2.0 


7 


2.4 


2.3 


8 


2.f 


2.5 


9 


3-1 


3-0 


10 


.3-4 


3-3 


20 


6.8 


6.6 


30 


10.2 


lo.o 


40 


13-6 


13-3 


50 


17.1 


16.6 



P. p. 



19 

1-9 
2-3 
2.6 

2.9 

3-2 

6.5 

9-7 
13.0 
16.2 





8 


8 


6 


0.8 


0.8 


7 


I.O 


O.q 


8 


I.I 


1.0 


9 


1-3 


1.2 


10 


1.4 


1-3 


20 


2-8 


2-6 


30 


4.2 


4.0 


40 


S-6 


5-3 


50 


7.1 


6.6 



0.7 
0.9 

1.0 
I.I 

1.2 
2-5 

3-7 
5.0 



57' 



60 



TABLE IV. 



33^ 



liOf;. Sill. 



5 
6 

7 
8 

9 

10 

II 

12 

13 
14 



15 
i6 

17 
i8 

'9 



20 

21 



25 
26 

27 
28 
29 



30 

3' 

32 
33 
34 



35 
36 
37 
38 
39 



40 

41 
42 

43 

44 



45 
46 

47 
48 

49 



oO 

51 
52 
53 
54 

55 
56 
57 
58 
59 
60 



73611 
73630 
73650 
73 669 
73688 



73708 
73727 
73 746 
73766 
73 78§ 



73805 
73824 

73843 
73862 
73 8S2 



73901 
73920 
73940 
73 959 
73 978 



73 997 
74016 
74036 
74055 
74074 



74093 
74 112 

74 131 
74 151 
74170 



74189 
74 208 
74227 
74246 
74265 



74284 

74303 
74322 

74341 
74360 



74 379 
74398 
74417 
74436 
74 455 



74 474 
74 493 
74 511 
74530 
74 549 



74568 
74587 
74606 
74625 
74643 



74662 
74681 
74700 
74718 
74 73^ 
9-74756 
Log. Cos. 



Lop. Tan. 



251 
279 
307 

334 
362 



390 
417 
445 
473 
506 



528 
555 
583 
616 

638 



666 

693 
721 

748 
776 



803 
831 
858 
886 

913 



941 
968 
996 
82 023 
82051 



82 078 
82 105 
82 133 
82 166 
82188 



8221I 
82243 
82 276 
82 29^ 
82325 



82352 
82380 
82407 

82434 
82462 



82489 
82516 
82544 
82571 
82598 



82626 
82653 
82686 
82708 
82735 



82 762 
82789 
82817 
82844 
82871 
9- 82 898 
Log. Cot. 



r. (I. I,oe. Cot. 



28 
2? 
2f 
28 



2f 



2? 
27 
27 
2? 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 

27 
27 
27 
27 
27 
27 
27 
27 
27 
27 

27 
27 
27 
27 
27 

27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
cTdT 



8 748 
8 726 

8693 
8 66§ 
863? 



8 610 
8582 

8555 
8527 
8499 



8472 
8444 
8417 
8389 
8362 



8334 
8306 
8279 
8 251 
8224 



8 196 
8 169 
8 14T 
8 114 
8086 



8059 
8031 
8 004 
7 976 
7 949 



7921 
7894 
7867 

7839 
7812 



7784 
7 757 
7729 
7 702 
7675 



7647 
7 620 

7 593 
7 56§ 
7538 



7510 
7483 
7456 
7 428 
7401 



7 374 
7 347 

7319 
7 292 
7265 



7 22,7 
7 216 
7183 
7 156 
7 128 

7 lOI 
Log. Tan. 



Log. Cos. 
92 359 
92351 
92342 

92334 
92326 




92318 
92310 
92 301 
92293 
92285 



92 
92 
92094 
92085 
92 077 



92 069 
92 060 
92 052 
92043 
92035 



92 027 
92018 
92 010 
92 ooT 
91 993 



984 
976 
967 
959 
951 



942 
934 
925 
917 

908 



900 
891 
883 
874 
866 

9.91 85? 
Log . Sill. 



(JO 

59 
58 
57 
Ji 
55 
54 
53 
52 
5' 
60 
49 
48 
47 
46 



45 
44 
43 
42 
41 
40 
39 
38 
37 
36 



35 
34 
33 
32 
31 
30 
29 
28 
27 
26 



25 
24 

23 

22 
21 

"20 

19 
18 

17 
16 



15 

14 
13 
12 
1 1 

To 

9 

8 

7 
6 





28 


21 


6 


2.8 


2.7 


7 


3-2 


3-2 


8 


Z-f 


3-6 


9 


4.2 


4.1 


10 


4-6 


4.6 


20 


9-3 


9.1 


30 


14.0 


l^.1 


40 


18.6 


18.3 


50 


23-3 


22.9 



27 

2.7 

3-1 
3-6 
4.0 

4-5 
9.0 

13-5 
18.0 

22.5 





19 


19 


6 


1.9 


1.9 


7 


2.3 


2.2 


8 


2.6 


2.5 


9 


2.9 


2.8 


10 


3-2 


3-1 


20 


6.5 


6.3 


30 


9-1 


9.5 


40 


13.0 


12.6 


50 


16.2 


iS-8 



18 

1-8 
2.1 

2.4 
2.8 

3-1 

6.1 

9.2 

12.3 

15.4 





8 


6 


0.8 


7 


I.O 


8 


I.I 


9 


1-3 


10 


1.4 


20 


2.8 


30 


4.2 


40 


5-6 


50 


7-1 



8 

0.8 
0.9 
1.6 
1.2 
1-3 
2.8 
4.0 

5-3 
6.6 



p. P. 



56'' 



6i 



34' 



TABLE IV. 



3 

4 

5 
6 

7 
8 

9 
10 

II 

12 

13 

14 

15 
i6 

17 
i8 

19 



20 

21 

22 
23 
24 

25 
26 
27 
28 
29 

30 

31 

32 
33 
34 



35 
36 
37 
38 
39 



40 

41 
42 
43 
44 



45 
46 

47 
48 

49 
50 

51 

52 
53 
54 

55 
56 
57 
58 
59 
60 



Log. Sin. 

74756 
74 775 
74 793 
74812 

74831 



74849 
74868 
74887 
74905 
74924 

74 943 
74961 
74980 
74 998 
75017 



75036 
75054 
75073 
75091 

75 no 



75 128 
75 147 
75i6§ 
75 184 
75 202 



75 221 
75239 

7525? 
75276 
75 294 



75313 
75331 
75 349 
75368 
75386 



75404 
75423 
75441 
75 459 
75478 



75496 
75514 
75532 
75551 
75569 



75587 
75605 
75623 
75642 
75 660 



75678 
75696 
75714 
75732 
75750 
75769 
75787 
75805 
75823 
75841 



975859 

Log. Cos. 



Log. Tan. 



82898 
82926 

82953 
82986 
8300? 



83035 
83 062 
83089 

83 116 
83 143 



83 171 
83198 
83225 
83 252 
83279 



83307 
83334 
83361 
83388 
8341? 



83442 
83469 
83496 
83524 
83551 



83578 
83605 
83632 

83659 
83686 



83713 
83740 
83767 
83794 
83821 



83848 
83875 
83 902 
83929 
83957 



83984 
84 01 1 
84038 
84065 
84 091 



84 118 
84145 
84 172 
84199 
84226 



84253 
84286 

8430? 
84334 
84361 



84388 
84415 
84 442 
84469 
84496 
84 522 
Log. Cot. 



c. d. 

2? 
27 
2? 
27 
2? 
27 
2? 
27 
27 
2? 
27 
2? 
27 

27 
2? 
27 
27 
27 

2? 
27 
27 
27 
2? 
27 
27 
27 
27 
2? 
27 
27 
27 
27 

27 
27 

27 
27 
27 

27 
2? 
27 
27 
27 
27 
26 
27 
27 

27 
27 

27 
27 
27 
27 
27 
26 

27 
27 

27 
27 

27 

26 



Log. Cot. 
7 loi 
7074 
7047 
7019 
6 992 



6965 
6938 
6 916 
6883 
6856 



6829 
6802 
6774 

674? 
6 726 



6 693 
6 666 
6639 
6 612 
6584 



655? 
6530 
6503 
6476 
6449 



6422 

6395 
6368 

6340 

6313 



6286 
6259 
6 232 
6 205 
6 178 



6 15T 

6 124 
6 09^ 
6076 
6043 




5 746 
5719 
5692 
5665 
1639 
5 612 
5585 
5558 
5531 
550 4 

5 47^ 

Log. Tan. 



Log . Cos. 

9-9 

9-9 

9-9 

9-9 

9-9 



9-9 
9.9 
9.9 
9-9 
9-9 



9-9 
9-9 
9-9 
9.9 

9-9 



9-9 
9-9 
9-9 
9.9 
9.9 



9-9 
9.9 

9-9 
9-9 
9-9 



9.9 
9-9 
9-9 
9.9 

9-9 



9.9 

9-9 
9.9 

9-9 
9-9 



9-9 
9-9 
9.9 

9-9 
9-9 



9-9 
9.9 
9.9 
9-9 
9-9 



9-9 
9-9 
9.9 

9-9 
9-9 



857 
849 
846 
832 
823 



814 
806 
19l 
789 
786 



772 
763 
755 
746 
73? 



729 
726 
712 

694 



686 
67? 
668 
660 
651 



642 

634 
625 

616 
608 



599 
590 
582 

573 
564 



556 
547 
538 
529 
521 



512 
503 
495 
486 

Ml 



460 

451 
442 
433 




9-91 336 

Log. Sin. 



d. 




_ 


GO 


8 


59 


8 
8 


58 

57 


8 


56 


9 

8 
8 
8 


55 
54 


53 
52 
5' 


8 


S 
8 
8 
9 
8 


50 


49 


48 


47 


46 


8 
8 
8 
9 
8 


45 


44 


43 
42 

41 


8 
8 


40 


39 


9 
8 


38 


37 


8 


36 


9 
8 
8 


35 


34 


33 


9 


32 


8 


31 


8 


30 


9 


29 


8 


28 


8 


27 


9 


26 


S 


25 


9 
8 


24 


23 


9 


00 


8 


21 


8 


20 


9 


19 


8 


18 


9 


17 


8 


16 


9 


15 


8 


14 


9 


13 


9 


12 


8 


II 


9 


10 


8 


9 


9 


8 


9 


7 


8 


6 


9 


5 


8 


4 


9 


3 


9 


2 


8 


I 


9 





d. 


/ 



P. p. 





2f 


27 


2e 


6 


2.? 


2.7 


2. 


7 


3-2 


3-1 


3- 


8 


3-6 


3-6 


3- 


9 


4.1 


4.0 


4- 


10 


4.6 


4-5 


4- 


20 


9.1 


9.0 


8. 


30 


13-7 


13-5 


13- 


40 


18.3 


18.0 


17- 


50 


22.9 


22.5 


22. 





19 


18 


6 


1-9 


1-8 


7 


2.2 


2.1 


8 


2.5 


2.4 


9 


2.8 


2.8 


10 


3-1 


3.1 


20 


6.3 


6.T 


30 


9-5 


9.2 


40 


12.6 


12.3 


50 


15-8 


15-4 



18 

1.8 
2.1 
2.4 
2.7 
30 
6.0 
9.0 
12.0 
15.0 





9 


6 


0.9 


7 


I.O 


8 


1.2 


9 


1-3 


10 


1-5 


20 


3-0 


30 


4-5 


40 


6.0 


50 


7-5 



8 

0.8 
1.0 
1. 1 
1-3 
1-4 
2-8 

4-2 

5-6 
7-1 



P. P. 



55° 



62 



TABLE IV. 



35^ 



Imh. Sill. 



5 
6 

7 
8 

9 

10 

II 

12 

13 
14 

15 
i6 

17 
i8 

19 



20 

21 



-0 

Ji. 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 



35 
36 
37 
38 

39 



40 

41 

42 

43 
44 

45 
46 

47 
48 

49 

50 

51 

52 
53 
54 

55 
56 
57 
58 
59 



GO 



75 859 
75877 
75895 
75913 
75931 



75 949 
75967 
75985 
76003 
76021 



76039 
76057 
76075 
76092 
76 II 6 



76 128 

76 i4d 
76 164 
76 182 
76 200 



7621^ 
7623! 
76253 
76271 
76 289 



76306 
76324 
76342 
76 360 

76377 



7639? 
76413- 
76431 
76448 
76466 



764S4 
76 501 
76519 
76536 
76554 



76572 
76589 
76607 
76 624 
76642 



76660 
76677 
76695 
76 712 
76730 



76 7\1 
76765 
76782 
76 800 
76817 



76835 
76852 
76869 
76887 
76904 



769: 



Log. Cos. 



Lot;. Tan. r. d. 



84532 
84 549 
84576 
84603 
84630 



84657 
84684 

84711 
8473? 
84764 



84791 
84818 

84845 
84871 

84898 



84 92§ 
84952 

84979 
85005 
85032 



85059 
85086 
85 113 
85 139 
85166 



85 193 
85 220 

85246 

85273 
8; ^00 



85327 
85353 
85380 
85407 
85433 



85 466 
85487 
85513 
85 546 
85567 



85 594 
85620 

85647 
85673 
85 700 



85727 

85753 
85786 
85807 
85833 



85860 
85887 

85913 
85940 

85966 



9-85 993 
9.86 020 
9.86046 
9.86073 
9. 86 099 



126 



27 

27 
27 

26 

27 
27 

27 

26 

27 
27 

26 

27 

26 

27 
27 

26 

27 

26 

27 
27 

26 

27 

26 

27 

26 

27 

26 

27 

26 

27 

26 
2g 

27 

26 

27 

26 
26 

27 

26 

27 

26 
26 
26 

27 

26 
26 

27 

26 
26 
26 

27 

26 
26 
26 
26 

27 

26 
26 
26 
26 



I.oir. Cot. 




5208 

5 182 
5 155 
5 128 
5 loT 



5074 
5048 

5 021 
4 994 
496? 



4940 
4914 
4887 
4860 

4833 



4807 
4780 
4753 
4 726 
4700 



4673 
4646 
4620 

4 593 
4566 



4 539 
4513 
4486 
4459 

4 433 



4406 
4 379 
4 353 
4326 
4299 



4273 
4 246 
4219 

4 193 
4 166 



4140 

4113 
4086 
4 060 
4033 



4007 
3980 
3 953 
3927 
3906 



0.13874 



Log. Cot. I c. d. I Log. Tan. 



I.oc. Cos. 

336 
V-1 
318 
310 
301 
292 
283 
274 

26| 

256 



9.9 
9-9 
9-9 
9-9 
9:9 

9-9 
9.9 
9.9 

9-9 
9.9 



9-9 
9.9 

9-9 
9-9 
9-9 



9-9 
9-9 
9-9 
9-9 
9.9 



9.9 
9-9 
9-9 
9.9 

9-9 

9-9 
9-9 
9-9 



247 
239 
230 
221 
212 



203 
94 
8S 
76 
6? 



13 

04 

095 

086 

077 



068 
059 
050 
041 
032 



023 
014 
00^ 
9.90996 
9.90987 



9.90978 
9.90969 
9.90 960 
9.90951 
9.90942 



990933 
9.90923 
9.90914 
9.90905 
9.90896 



9.9088^ 
9.90878 
9.90 869 
9. 90 860 
9.90 850 



9.90 841 
9.90832 
9.90823 
9.90 814 
9.90 805 



9.90796 



Log. Sill. 



(50 

59 
58 
57 

55 
54 
53 
52 
5' 
50 
49 
48 
47 
46 



45 
44 
43 
42 

41 
40 

39 
38 
37 
36 



15 
14 
13 
12 
1 1 

To 

9 

8 

7 
6 





27 


2S 


6 


2.7 


2.6 


7 


.3-1 


.31 


8 


3-6 


3§ 


9 


4.0 


4.0 


10 


4-5 


4-4 


20 


9.0 


8.8 


30 


13 5 


13.2 


40 


18.0 


17-6 


50 


22.5 


22.1 





18 


i^ 


6 


1.8 


1-7 


7 


2.1 


2.0 


8 


2.4 


2.3 


9 


2.7 


2.6 


10 


30 


2.9 


20 


6.0 


5-8 


30 


9.0 


8.7 


40 


12.0 


II. 6 


50 


15.0 


14.6 



17 

1-7 
2.0 

2.2 

2.§ 
2-8 

5.6 
8.5 

II-3 
14.1 





9 


9 


6 


0.9 


0.9 


7 


I.I 


I.O 


8 


1.2 


1.2 


9 


1.4 


1-3 


10 


1.6 


i-S 


20 


31 


30 


30 


4.y 


4-5 


40 


6.3 


6.0 


50 


7-9 


7.5 



8 

0.8 
1.0 
I.I 

1-3 

1.4 

2-8 

4.2 

5-6 
7.1 



p. I' 



54^ 



36^ 



TABLE IV. 



20 

21 



24 



25 
26 
27 
28 
29 



30 

31 

32 
33 

34 

35 
36 
37 
38 
39 



40 

41 

42 

43 
44 



45 
46 

47 
48 

49 
50 

51 
52 
53 

54 



55 
56 
57 
58 
59 



«0 



Log. Sin. 
9.76 922 
9.76939 

9-76956 
9.76974 

9-76991 



9.77 008 
9.77026 

9-77043 
9.77 066 
9.77078 



9.77095 
9.77 112 
9.77 130 
9.77147 
9.77 164 



9.77 iSi 

9-77 198 
9.77 216 
9-77233 
9.77250 



9.77 26^ 
9-77 284 
9.77302 
9-77319 
9-77 336 



9-77 353 
9-77 370 
9-77387 
9-77404 
9.77421 



9-77 439 
9-77456 

9-77 473 
9.77490 

9-77 507 



9-77 524 
9-77 541 
9-77558 
9-77 575 
9-77 592 



9-77609 
9.77 626 

9-77643 
9.77 660 

9-77677 



9.77693 
9.77710 
9-7772^ 
9-77 744 
9.77761 



9.77778 

9-77 795 
9.77 812 
9.77828 
9-7784? 



9.77 862 

9-77879 
9-77896 

9-77913 
9.77929 



9-77 946 

Log. Cos. 



Log. Tan. 
9. 86 1 26 
9.86 152 
9.86 179 
9. 86 206 
9.86 232 



9.86 259 
9.86285 
9.86 312 
9-86338 
9-86365 



9.86 391 
9.86418 
9-86444 
9.86471 
9-8649? 



9.86524 
9.86 550 

9-86577 
9. 86 603 
9.86 630 



9.86655 
9.86683 
9.86 709 
9-86736 
9.86762 



9.86788 
9.86815 
9.86841 
9.86868 
9.86894 



9.86 921 
9.86947 
9.86973 

9.87 000 
9.87025 



9.87053 
9.87079 
9.87 105 
9.87 132 
9-87 158 



9.87 185 
9.87 211 
9-8723? 
9.87 264 
9.87 290 



9-87 316 
9-87343 
9.87369 

9-87395 
9.87 422 



9-87 448 
9-87474 
9.87501 

9-87 52? 
9-87 553 



9.87 580 
9. 87 606 
9.87 632 
9.87659 
9.87685 

9-87711 

Log. Cot. 



c. d. 



26 

26 

27 

26 
26 
2§ 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 

26 

26 
26 
26 
26 
26 
26 

26 

26 
26 
26 
2S 

26 

26 
26 
26 

26 

26 
26 
26 

26 

26 
26 

26 

2§ 
26 

26 

26 
26 

26 

26 
26 

26 

26 

26 

2§ 
cTdT 



Log. Cot. 



0.13874 
0.1384^ 

0.13 821 

0.13794 
0.13767 



0.13741 
O.I37I4 

0.13 688 
0.13 661 

0.13635 



o. 1 3 608 

0.13 582 

0.13555 
0.13 529 

o. 1 3 502 



0.13476 
0.13449 
0.13423 

0.13 396 

0.13370 



Log. Cos. 



9.90796 
9.90785 
9.90777 

9.90 768 

9.90759 



9.90750 
9.90746 
990731 

9.90 722 

9.90713 



9.90703 
9.90694 

9.90685 
9.90676 

9.90665 



0.13343 
0.13 317 

0.13 290 
0.13 264 

0.13237 



O. I 3 211 

0.13 185 
0.13 158 

0.13 132 
0.13 105 



0.13079 

0.13 052 

0.13025 

o. 1 3 000 

0.12973 



o. 1 2 947 
0.12 920 

O. I 2 894 

0.12868 

O. 12 841 



O. I 2 815 
O. 12 789 
O. 12 762 

0.12736 

O. 12 709 



0.12 683 
0.12 657 

O. 12 636 
O. I 2 604 

0.12 578 



0.12 551 

O. 12 525 

0.12 499 

O. 12 472 

O.I 2 446 



O. I 2 420 

0.12393 

O. 12 367 

0.12 341 

0-I23I5 

O. 12 288 
Log. Tan. 



9.9065^ 

9.90648 

9.90639 

9.90 629 
9.90620 



9.90 61 1 
9.90 602 

9.90592 
9.90583 

9-90 574 



9.90564 
9.90555 
9.90546 

9-90 536 

9.90 527 



9.90 518 

9-90508 
9-90499 
9.90490 

9. 90 480 



9.90471 

9. 90 461 

9.90452 
9-90443 
9-90433 



9.90424 
9.90414 
9-90405 
9.90396 

9-90386 



9.90377 
9-9036? 
9-90358 

9-90 348 

9-90339 



9.90330 
9-90320 
9.90 311 
9.90301 

9.90 292 



9.90 282 

9.90 273 

9.90 263 

9.90254 

9- 90 244 

9 90235 
Log. Sin. 



(>0 

59 

58 

57 

55 
54 
53 
52 
51 
oO 
49 
48 

47 

45 
44 
43 
42 

AL 
40 

39 
38 
37 
_3^ 
35 
34 
33 
32 
31 
30 

29 
28 

27 
26 



25 
24 
23 
22 
21 

"20 

19 
18 

17 
16 



p. p. 



15 
14 
13 
12 
II 

To 

9 

8 

7 
6 





27 


26 


6 


2.7 


2.6 


7 


3-1 


3-1 


8 


3-6 


3-5 


9 


4.0 


4.0 


10 


4-5 


4.4 


20 


9-0 


8.8 


30 


13-5 


13-2 


40 


18.0 


17-6 


50 


22.5 


22.1 



6 

7 
8 

9 
10 
20 
30 
40 
50 



If 

I-? 
2.0 

2-3 
2.6 

2-9 

5-8 

8.? 

II. 6 

14.6 



17 

1-7 
2.0 
2.2 

2.§ 
2.8 

5.§ 

8.5 

II. 3 

14.1 



6 

7 
8 

9 
10 
20 
30 
40 
50 



9 

0.9 
I.I 

1.2 
1.4 
1.6 
3-1 

4-7 
6-3 
7.9 



26 

2.6 
3-0 
3-4 
3-9 
4-3 
8.6 
13.0 

17.3 
21.6 



18 

1.6 
1-9 

2. 2 

2.5 
2.? 

5.5 
8.2 

II. o 

13.? 



9 

0.9 
i.o 
1.2 
1.3 
1-5 
3-0 

4-5 
6.0 

7-5 



P. P. 



53' 



64 



TABLE IV. 



37^ 



10 

II 

12 

13 

15 
i6 

17 
i8 

'9 



20 

21 
22 
23 
24 



25 
26 

27 
28 

29 

30 

31 
32 
33 
34 

35 
36 
37 
38 
39 



40 

41 
42 
43 

44 

45 
46 

47 
48 

49 

50 

51 

52 
53 
54 

55 
56 
57 
58 
59 



60 



1,011. Sill. 

9-77 946 
9-77963 
9.77 980 

9-77 996 
9.78013 



9.78 030 

9.78046 
9.78063 
9.78 080 
9.78097 



9.78 113 
9.78 130 
9.78 147 
9.78 163 
9.78 180 



9.78 196 
9.78213 
9.78230 
9.78246 
9.78263 



9.78279 
9.78296 
9.78 312 
9.78329 
9.78346 



9.78362 
9-78379 
9-7839? 
9.78412 
9.78428 



9.78444 
9.78461 
9.7847; 
9.78494 
9.78510 



9.78527 
9-78 543 
9-78 559 
9.78576 
9.78592 



9.78 609 
9.78625 
9.78 641 
9.78658 
9.78674 



9.78 696 
9.78707 
9.78723 
9-78739 
9-78755 



9-78772 
9-78788 
9.78 804 
9.78821 
9.78837 



9-78853 
9.78 869 
9.78885 
9.78 902 
9.78918 



9-78934 
Log. Cos. 



d. 



liOi;. 'I'liii. <-. il 



9.87 
9.87 
9.87 
9.87 

9:31 



9.87 
9.87 
9-87 
9-87 
9-87 



711 

73^ 
764 
796 
816 

843 
869 
895 
921 
948 



9-87 
9.88 
9.88 
9.88 
9.88 



974 
006 

026 

053 
079 



9.88 
9.88 
9.88 
9.88 
9.88 



105 

131 

15? 
184 

210 



9.88 
9.88 
9.88 
9.88 
9.88 
9.88 
9.88 
9.88 
9.88 
9.88 



236 
262 

288 
315 
341 

367 
393 
419 

44§ 
472 



9.88 
9.88 
9.88 
9.88 



524 
550 
576 
602 



).88 
1.88 
1.88 



629 

655 
681 
707 
733 



88 



759 
78? 
81T 



9.88 
9.88 
9.88 
9.88 



890 
916 
942 
968 

994 



).89 

1.89 

1.89 

89 



9 

6 9-89 

2 9-89 

6 9-89 

16 9.89 

16 



020 

046 
072 

098 
124 



150 
177 
203 
229 

255 



9.89281 
Log. Cot. 



26 
26 
26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 



26 

26 

26 

26 

26 

26 
26 

26 

26 
26 

26 

26 
26 

26 

26 
26 

26 

26 
26 

26 

26 
26 
26 

26 

26 
26 
26 

26 

26 
26 
26 
26 
26 

26 

26 
26 
26 
26 
26 
26 

26 

26 
26 
26 
26 

c. «J. 



2288 

2 262 
2 236 

2209 

2 183 



2 157 

2 13' 
2 104 

2 078 

2 052 
2 026 

999 
973 
947 
921 



895 
868 
842 
816 
790 



763 

73/ 
711 
685 
659 



633 
606 

580 

55-? 
528 



502 
476 
449 
423 
39^ 
371 
345 
319 
293 
266 



240 
214 
188 
162 
136 



1 10 
084 
058 
032 
005 



0979 

0953 
0927 
o 901 
0875 



o 849 

0823 
0797 
0771 
0745 



o. 10 719 

Log. Tan. 



Loif. Cos. 
90 235 



90 225 
90 216 
902O6 
90196 



90 187 

9017? 
90 168 

90158 
90 149 



90139 
90130 
90 120 
90 116 
90 lOI 



90091 
90082 
90072 
90062 

90053 



90043 
90033 

90024 
90014 
90004 



89995 
89985 

89975 
89966 

89956 



89946 
89937 
89927 
89917 
89908 

89"898" 
89888 
89878 
89869 
89S59 



89 849 
89839 
89830 
89820 
89810 



89806 
89791 
89781 
89771 
89 761 



89751 
89742 
89732 
89 722 
89 712 



89 702 
89 692 
89683 
89673 
89663 



989653 



Loir. Sill. 



9 

9 

9 

10 

9 
9 
9 
9 
9 
9 
9 
10 

9 
9 
9 

9 
10 

9 
9 

9 
10 

9 

9 

10 

9 

9 
10 

9 

9 
10 

9 

9 
10 

9 
10 

9 
10 

9 
10 

9 
10 

9 
10 

9 
10 

9 

lO- 

10 

9 

10 

9 
10 
10 

9 
10 
10 

9 
10 
10 
10 



<>0 

59 
58 
57 

55 
54 
53 
52 
5' 
50 

49 
48 

47 

45 
44 
43 
42 
41 
40 
39 
38 
37 
J^ 
35 
34 
33 
32 
31 
30 

29 
28 
27 
26 



25 
24 

23 
22 
21 

"20 

19 
18 

17 

16 



15 
14 
13 
12 
1 1 

To 

9 

8 

7 
6 



2§ 26 



6 

7 
8 

9 
10 
20 

30 
40 

50 



2.6 


2. 


3-1 


3- 


3-5 


3- 


4.0 


3- 


4.4 


4- 


8.8 


8. 


13.2 


13- 


17-6 


17- 


22.1 


21. 





17 


18 


6 


1-7 


1-6 


7 


2.0 


1.9 


8 


2.2 


2.2 


9 


2.§ 


2.5 


10 


2.8 


2.'7 


20 


5.6 


5-5 


30 


8.5 


8.2 


40 


II-3 


11,0 


50 


14. 1 


13-7 



16 

1.6 

1-8 
2.1 
2.4 
2.6 

5-3 
8.0 

lO.g 

13-3 



10 



6 

7 
8 

9 

10 
20 

30 
40 

50 










I 




3 




5 




6 


3 


3 


5 





6 


6 


8 


3 



9 

0.9 
I.I 
1.2 
1.4 
1.6 
3-1 
4.7 
6.3 
7.9 



p. 1' 



52^ 



65 



38^ 



TABLE IV. 



10 

II 

12 

13 
14 



15 
16 

18 
19 



20 

21 



Log. Sin. 

9-78934 
9.78956 
9.78965 
9.78982 
9.78999 



9.79015 
9.79031 
9.79047 
9.79063 
9.79079 



9.79095 

9.79 III 
9.79 127 

9-79 143 
9.79159 



9.79175 
9-79191 
9-7920? 
9.79223 
9.79239 



25 
26 
27 
28 
29 
30 
31 
32 
33 
34 

35 
36 
37 
38 
39 



40 

41 
42 
43 
44 

45 
46 

47 
48 

A9_ 
50 
51 
52 
53 
54 



55 
56 
57 
58 
59 
60 



9.79255 
9.79271 
9.79287 
9.79303 
9 79319 



9-79 33? 
9-79351 
9-79367 
9-79383 
9-79 399 



9-79415 
9-79431 
9-79 446 
9.79462 

979 478 

9-79 494 
9.79510 
9.79526 
9-79541 
9-79 557 



9-79 573 
9-79589 
9.79605 
9.79 620 
9-79636 



9.79652 
9.-^9 668 
9-79683 
9.79699 
9.79715 



9.79730 

9-79 746 
9.79762 

9-79 777 
9-79 793 



9-79809 
9.79824 
9.79840 
9.79856 
9.79871 



9-79887 

Log. Cos. 



d. 

16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 

15 
16 

16 
16 

15 
16 
16 

16 
16 

i; 

16 

16 

I? 
16 

15 
16 

15 
16 

15 
16 

iS 

i! 
16 

i§ 
i§ 
16 

I? 

i! 
16 

15 
15 
15 



Log. Tan. 
9.89 281 
9.89307 

9-89 333 
9-89359 
9.89385 



9.89 41 1 

9-89437 
9.89463 
9.89489 
9.89515 



9.89541 
9.89 567 

9-89 593 
9.89 619 

9-89645 



9.89671 
9.89697 
9.89723 
9.89749 
9.89775 



9.89 801 
9.89827 
9.89853 
9.89879 
9.89905 



9.89931 
9.89957 

9.89 982 

9. 90 008 
9.90034 



9.90 066 
9.90086 
9. 90 112 

990 138 
9.90 164 



9.90 190 
9.90 216 
9.90 242 
9.90 268 
9.90 294 



9.90319 

9-90 34? 
9.90371 
9.90 39f 
9.90423 



9.90449 

9.90475 
9.90 501 
9.90 526 
9.90552 



9-90578 
9. 90 604 
9.90630 
9.90 656 
9.90 682 



c. d. 



9.90707 

9-90733 
9.90759 
9.90785 
9.90 811 

9-90837 

Log. Cot. I e. d. 



26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 

2? 
26 
26 
26 
26 
26 
26 
2? 
26 
26 
26 
26 
26 

25 
26 
26 
26 
2§ 
26 
26 
26 
25 
26 

26 
26 

2! 
26 
26 

2$ 
26 
26 
26 
2? 
26 



Log. Cot. 



o.io 719 

0.10693 
O.IO 667 
O.IO 641 
o. 10 61 5 



o. 10 589 
o. 10 563 

0.10537 

O.IO 51 1 
o. 10485 



0.10459 

0.10433 

O.IO 407 
O.IO 381 

0.10355 



O.IO 329 

0.10303 

O.IO 277 
o. 10 251 
o. ro 225 



O.IO 199 
O.IO 173 
O.IO 147 

O.IO 121 

O.IO 095 



O.IO 069 
0.10043 
o. 10 017 
0.09 991 
0.09 965 



0.09 939 
009913 
0.09 887 
o.og 861 
0.09 836 



Lotr. Cos. 



9.89653 
9.89643 

9-89633 
9.89623 
9.89613 



9.89 604 
9.89594 
9.89584 
9.89574 
9.89564 



9.89554 
9.89544 

989534 
9.89524 
9.89514 



9.89504 
9.89494 
9.89484 
9.89474 

9 89 464 



9.89454 
9-89444 
9-89434 
9.89424 

9-89414 
9.89404 

9- 89 394 
9.89384 

989374 
9.89364 



0.09 810 
0.09 784 
0.09 758 
0.09 732 
0.09 706 



0.09 686 
0.09 654 
0.09 623 
0.09 602 
0-09 577 



0.09551 
0.09 525 
0.09 499 
0.09473 
0.09 447 



0.09 421 
0.09395 
0.09 370 
0.09344 
0.09 318 



9-89354 
9-89344 
9-89334 
9.89324 

9- '''9 314 



9-89304 
9.89294 
9.89284 
9.S9274 
9.89 264 



9.89253 
9.89243 

9-89233 
9.89223 
9.89213 



9.89203 
9.89193 
9.89182 
9.89 172 
9.89 162 



0.09 292 
0.09 26(5 
0.09 246 
o. 09 2 1 4 
0.09 189 



0.09 163 



Log. Tau. 



9.89152 
9.89142 
9.89132 
9.89 I 21 

9 89 1 1 1 



9.89 loT 
9.89 091 
9.89081 
9.89076 
9.89066 



050 



9 
10 
10 
10 

9 
10 
10 
10 
10 
10 

9 
10 
10 
10 
10 
10 
10 
10 
10 
10 
10 
10 
10 
10 
10 
10 
10 
10 
10 
10 
10 
10 
10 
16 
10 
10 
10 
10 
10 
16 
10 
10 
10 
16 
10 
10 
16 
10 
10 
10 
16 
10 
16 
10 
10 
16 
10 
16 
10 
10 



Log. Sin. I d. 



GO 

59 
58 
57 
56 



55 
54 
53 
52 
51 
50 
49 
48 
47 

45 
44 
43 
42 

41 



p. p. 



40 

39 
38 
37 
J^ 
35 
34 
33 
32 
31 



30 

29 
28 
27 
26 



25 

24 

23 
22 
21 

"20 

19 
18 

17 
16 

15 

14 
^3 
12 
1 1 

"lo 

9 
S 

7 
6 





26 


6 


2.6 


7 


.3-0 


8 


3-4 


9 


3-9 


10 


4-3 


20 


8-6 


30 


13.0 


40 


17.3 


50 


21.6 



2S 
2.5 

3-0 

3-4 
3-8 
4.2 
8.5 

12.? 
17.0 
21.2 





16 


16 


6 


1-6 


1.6 


7 
8 


1.9 
2.2 


1-8 
2.1 


9 


2-5 


2.4 


10 


2.7 


2-6 


20 
30 


5.5 
8.2 


5-3 
8.0 


40 


II. 


10.6 


50 


13-7 


^3-3 



15 

1.8 
2.6 

2-3 
2.6 

5-1 

7-7 

10.3 

12.9 





10 


10 


6 


1.6 


I.O 


7 


1.2 


I.I 


8 


1.4 


I-.3 


9 


1.6 


1.5 


10 


1-7 


1-6 


20 


3-5 


3-3 


30 


5.2 


5-0 


40 


7-0 


6.6 


50 


8.? 


8.3 



9 

0.9 
I.I 
1.2 
1.4 
1.6 
3-1 
4.7 
6.3 
7-9 



p. p 



51" 



66 



TABLE IV. 



39 



9 
10 

1 1 

12 

14 



liOi;. Sill. 



.79S87 
•79903 
799I8 

79 934 
79 949 



15 
16 

17 
18 

19 



20 

21 



25 
26 

27 

28 
_29 

30 

31 
32 
33 
34 



35 
36 
37 
38 
39 



40 

41 

42 
43 
44 



45 
46 

47 
48 

49 



50 

51 

52 
53 
54 

55 
56 
57 
58 
59 
(JO 



.79965 
.79980 
.79996 
8001 1 
80037 



So 042 
80058 
80073 
80089 
80 104 



80 120 
80135 
80 151 
80 165 
80 r82 



9.80 197 
9.80 213 
9.80228 
9.80243 
9.80 259 



80274 
80289 
80305 
80 320 
8033? 



80351 
80366 
80381 
80397 
80412 



80427 
80443 
80458 

80473 
80 48 A 



9. 80 504 
9.80 519 
9.80534 
9.80549 
9.80 564 



9.80 580 

9.80595 

9.80610 

9.80625 

9. 80 646 

9^8065!" 

9.80671 

9.80686 

9.80 701 

9-80716 



9.80731 
9.80746 
9.80 761 
9.80776 
9.80 791 



9. 80 806 



liOg. Tau. 



9.90837 
9.90 863 
9.90883 
9.90914 
9.90940 



9.90966 
9.9099 



9-9 
9.9 

9-9 



9-9 
9-9 
9.9 
9.9 
9-9 



9.9 

9-9 
9.9 
9.9 
9.9 



9-9 
9-9 
9-9 
9.9 

9-9 



9-9 
9.9 

9-9 
9-9 
9-9 



9-9 
9-9 
9-9 
9.9 
9.9 



9.9 
9-9 
9-9 
9-9 
9-9 



9.9 
9-9 
9-9 
9.9 

9-9 



9-9 



01^ 

043 
069' 



095 
121 

Ho 
172 
198 



224 
250 

27§ 

30T 

327 



353 
378 
404 
430 
456 



481 
50? 
533 
559 
584 



610 
636 
662 
68^ 
713 



739 
765 

790 

816 

842 



867 

893 
919 

945 
970 



996 



9.92 022 

9.92 04? 
9.92073 
9.92099 



9.92 124 
9.92 150 
9.92 176 
9.92 201 
9.92 22^ 



9.92253 
9.92 278 
9.92 304 
9.92330 
9-92 35§ 



Lo^. Cos. 



9.92 381 



26 

25 
26 

2S 
26 
26 

2§ 
26 
26 

25 
26 

2S 
26 

25 
26 
26 

2S 
26 

25 
26 

25 
26 

2S 
26 

2! 
26 

2§ 
26 

2§ 
26 

2S 

26 

2§ 
26 

2S 
26 

2? 
26 

2! 
2? 
26 

2§ 
26 

2S 
25 
26 

2§ 
26 

25 
25 
26 
2? 
2§ 
26 

2§ 
2§ 
26 

2§ 
2§ 
26 



d. Lo^. Cot. I c. d. 



[/Ojr. Cot. 



0.09 163 
0.09 137 
0.09 1 11 
0.09085 
0.09060 



0.09034 
0.09008 
0.08 982 
0.08956 
0.08 936 

0.08 905 
0.08 879 
0.08 853 
0.08 827 
0.08 802 



0.08 776 
0.08 750 
0.08 724 
0.08 698 
0.08 673 



\,oe. Cos. 



9.89056 
9. 89 040 
9.89030 
9.89019 
9. 89 009 



9.88999 
9.88 989 
9.88978 
9.88968 
9.88 958 



0.08 647 
0.08 621 
0.08 595 
0.08 570 
0.08 544 



0.08 518 
0.08 492 
0.08 467 
0.08 441 
0.08 41 § 



0.08 389 
0.08 364 
0.08 338 
0.08 312 
0.08 28f, 



0.08 261 
0.08 235 
0.08 209 

0.08 183 
0.08 158 



0.08 132 
0.08 log 
0.08 081 
0.08 055 
0.08 029 



0.08 004 
0.07 978 
0.07 952 

0.07 926 

0.07 901 



0.07 875 
0.07 849 
0.07 824 
0.07 798 
0.07 772 



9.88947 
9.88937 
9.88 927 
9.88 917 
9-88 906 
9.88896 
9.88886 
9.88875 
9.88865 
9.88 855 
9.88 844 
9.88834 
9.88823 
9.88813 
9.88803 
9.88 792 
9.88782 
9.88772 
9.88761 
9-88751 



9. 88 746 
9.88730 
9.88720 
9.88 709 
9.88699 



0.07 747 
0.07 721 
0.07 695 
0.07 670 
0.07 644 



0.07 618 



Lo!?. Tun. 



9.88688 
9.88678 
9.8866? 
9.88657 
9-88 646 
9.88 636 
9.88625 
9.88615 
9.88604 
9-88594 
9-88 583 

9.88573 
9.88 562 
9.88552 
9.88 541 



9.88531 
9.88 526 
9.88 510 

9-88499 
9. 88 489 



9-88 478 
9.8846? 
9.88457 

9-88446 
9-88436 



9-88425 



Log. Sin. 



16 

10 

10 

10 

16 

10 

16 

10 

10 

16 

10 

10 

10 

16 

16 

10 

16 

10 

10 

10 

16 

10 

10 

16 

16 

10 

10 

16 

16 

16 

16 

10 

10 

16 

10 

10 

16 

16 

10 

16 

10 

10 

16 

10 

10 

10 

16 

16 

16 

16 

16 

10 

10 

16 

10 

II 

10 

16 

16 

16 



(iO 

59 
58 
57 
56 



55 
54 
53 

52 

50 

49 
48 

47 
_46 

45 
44 
43 
42 
41 
40 
39 
38 
37 
_3^ 
35 
34 
33 
32 
31 
30 
29 
28 
27 
26 



25 

24 
23 
22 
21 

Ho 

19 
18 

17 
16 

15 
14 
13 
12 
II 

lo 

9 
8 

7 
6 



6 

7 
8 

9 
10 
20 
30 
40 
50 



26 

2.6 
3-3 
3-4 
3-9 
4-3 
8.6 
13.0 

17.3 
21.6 



2S 





16 


IS 


6 


1.6 


I.^ 


7 


1-8 


1.8 


8 


2.1 


2.0 


9 


2.4 


2-3 


10 


2.6 


2.6 


20 


5-. 3 


5-1 


30 


8.0 


7.9 


40 


10.6 


10.3 


50 


13-3 


12.9 



15 

1-5 

I.? 
2.0 
2.2 

2.5 
5.0 

7.5 

lO.O 

12.5 





II 


16 


6 


I.I 


I.O 


7 


1-3 


1.2 


8 


1.4 


1.4 


9 


1-6 


1.6 


10 


1-8 


1-7 


20 


3.6 


3-5 


30 


5-5 


5.2 


40 


7-3 


7.0 


50 


9.1 


8.? 



10 

1.0 
1. 1 
1-3 
1-5 
1-6 
3-3 
5-0 
6.6 
8.3 



50° 



p. p. 



67 



40^ 



TABLE IV. 



10 

II 

12 

13 

14 



15 
i6 

i8 
19 



20 

21 

22 

23 
24 



25 
26 
27 
28 
29 



30 

31 
32 
33 
34 



35 
36 
37 
38 
39 



40 

41 

42 
43 
44 

45 
46 

47 
48 

49 



50 

51 

52 
53 
54 

55 
56 
57 
58 
59 
60 



Lof;. Sill. 



9.80 805 
9.80822 
9.80837 
9.80852 
9.80867 



9.80882 
9.80897 
9.80 912 
9.80927 
9.80 942 



9.80957 

9.80 972 
9.80987 

9.81 001 
9.81 OI6 



9.8 
9.8 
9.8 
9.8 
9.8 



9.8 
9.8 
9.8 
9.8 
9.8 



9.8 
9.8 
9.8 
9.8 
9.8 



9.8 
9.8 
9.8 
9.8 
9.8 



9.8 
9.8 
9.8 
9.8 
9.8 



9.8 
9.8 
9.8 
9.8 
9.8 



9.8 
9.8 
9.8 
9.8 
9.8 



9.8 
9.8 
9.8 



9.8 
9.8 
9.8 
9.8 
9.8 



031 

046 
061 

076 
091 



106 
121 

136 
150 
165 



180 

195 
210 

225 
239 



254 
269 
284 
299 
313 



328 
343 
358 

372 
387 



402 
416 
431 
446 
466 



47§ 
490 
504 
519 
534 



548 
563 
578 
592 
607 



621 
636 
656 
665 
680 

694 

Log. Cos. 



I;opr. Tan. c. d 



9.92 381 
9.92407 
9.92432 

9-92 458 
9.92 484 



9.92 509 

9-92 535 
9.92 561 
9.92 586 
9.92 612 



9.92 638 
9.92 663 
9.92 689 
9.92714 
9.92 746 



9.92 766 
9.92 791 
9.92817 
9.92 842 
9.92868 



9.92894 
9.92919 
9.92 945 
9.92971 
9.92 996 



9.93 022 
9-9304? 
9-93073 
9-93 098 
9-93 124 



9.93 150 

9-93 17! 
9.93 201 

9-93 226 
9.93 252 



9.93 278 
9-93 303 
9-93 329 
9-93 354 
9-93 380 



9-93 405 
993431 
9-93 456 
9.93482 

9-93 508 



9-93 533 
9-93 559 
9-93 584 
9.93610 

9-^3635 



9.93 661 
9.93 686 
9.93712 
9-93 73? 
9-93763 



9-93 788 
9.93814 
9.93840 
9.93 86S 
9-93 891 

9-93 916 

Log. Cot. c. d 



25 
26 

25 

2§ 

2S 
26 

25 
2§ 
26 
25 
2S 
2§ 
26 

2§ 
25 
2? 
25 
26 

2§ 
25 
25 
26 

25 
25 
2§ 
25 
25 
26 

2§ 
2§ 
25 
2? 
25 
26 
25 
25 
25 
25 
2S 
25 
2§ 
25 
26 

25 
2! 
2§ 
2§ 
25 
2§ 
25 
25 
2§ 
25 
2! 
2! 
26 
2§ 
25 
25 



Log. Cot. 



0.07 618 
0.07 593 
0.07 56^ 
0.07 541 
0.07 516 



0.07 490 
0.07 465 
0.07 439 
0.07413 
0.07 388 



0.07 362 

0.07 336 
0.07 31 1 
0.07 285 
0.07 259 
0.07 234 

0.07 20§ 
0.07 183 
0.07 15? 
0.07 I 31 



0.07 106 
0.07 080 
0.07055 
0.07 029 
0.07 003 
0.06978 
0.06 952 
0.06 927 
0.06 90T 
0.0687? 



0.06 850 
0.06 824 
0.06 799 

0.06 773 
0.06 748 



0.06 722 
0.06 696 
0.06 671 
0.06 645 
0.06 620 



0.06 594 
0.06 569 
0.06 543 
0.06 518 
0.06 492 



0.06466 
0.06 441 
0.06 41 5 
0.06 390 
0.06 364 



0.06 339 
0.06 313 
0.06 288 
0.06 262 
0.06 237 



0.06 211 
0.06 186 
0.06 160 
0.06 134 
0.06 109 
0.06083 

Log. Tan. 



Log. Cos. 



88425 
88415 
88404 

393 
88383 




88319 
88308 
8829? 
88287 
88 276 



88265 
88255 
88244 
88233 
88223 



S8212 
88 201 
88 190 
88 180 
88 169 



88 158 
8814? 
88137 
88 126 
88ii§ 



88 104 
88094 
88083 
88072 
8 806T 
88056 
88039 
88029 
88018 
88007 



87996 
87985 
87974 
87963 

87953 



87942 

87931 
87 920 
87909 
87898 



87887 

87876 
87865 

87854 
87844 



87833 
87822 
87811 
87800 
87789 
9-87778 



Log. Sin. 



10 

II 

16 

10 

16 

I I 

10 

16 

I I 

10 

16 

II 

16 

16 

II 

16 

10 

II 

16 

II 

16 

II 

16 

II 

10 

II 

16 

I I 

16 

II 

10 

II 

II 

16 

II 

II 

16 

II 

II 

16 

II 

II 

II 

16 

II 

II 

II 

16 

II 

II 

II 

I I 

II 

16 

II 

II 

II 

II. 

II, 

II 



GO 

59 
58 
57 
56 



55 
54 
53 
52 
51 
50 

49 
48 

47 
46 



45 
44 
43 
42 

41 
40 

39 
38 
37 
36 



35 
34 
33 
32 
31 
30 

29 
28 

27 
26 



15 
14 
13 
12 
II 

To 

9 

8 

7 
6 



P. P. 





26 


6 


2.6 


7 


.30 


8 


3-4 


9 


3-9 


10 


4-3 


20 


8.6 


30 


13.0 


40 


17-3 


50 


21.6 



2S 

2.5 
30 

3-4 

3-8 

4.2 

8.5 

12.? 

17.0 

21.2 





iS 


15 


6 


I-§ 


1-5 


7 


1.8 


I-? 


8 


2.0 


2.0 


9 


2-3 


2.2 


10 


2.6 


2.5 


20 


5-f 


S.o 


30 


1.1 


7-5 


40 


10.3 


lO.O 


50 


12.9 


12.5 



14 

1.4 

1-7 
1.9 

2.2 
2.4 

4-8 
7.2 

9-6 
12. 1 





II 


6 


i.il 


7 




3 


8 




4 


9 




6 


10 




8 


20 


3 


6 


30 


5 


5 


40 


7 


3 


50 


9 


I 



3-5 
5.2 
7.0 
8.7 



p. p. 



49° 



6S 



TABLE IV. 








41° 














; 


LOK. sill. 


.1. 


l.oi;. Tiui. 


(-. .1. 


Loir. Cot. 


I.oir. t'ds. ,1. 




r. 1". 





9.81 694 


14 
14 
14 


9-93 9 '6 


2? 
2? 
2? 
25 
2§ 
2§ 
25 
2S 
2? 
25 
25 
25 
25 
25 
25 
25 
25 
25 
2§ 
2? 
2§ 
2? 
25 
2S 
2§ 
2$ 
2? 
25 
25 
2§ 
2? 
25 
25 
2S 
2? 
2§ 
25 
2§ 
2? 
25 
2§ 
25 
2? 
2§ 
2§ 
25 
2§ 
25 


0.06 083 


9 


87778 1 ,, 


(JO 




I 


9. Si 709 


993942 


0.06 058 


9 


87767 




59 




o 


9.81 723 


993967 


0.06032 


9 


87756 




58 




3 


9.81 73« 


9-93 993 


0.06 007 


9 


87745 




57 




4 


9.81 752 


9.94 018 
9-94044 


0.05 981 


9 


87734 




56 
55 




5 


9.81 767 


0.05 956 


9 


87723 


6 


9.81 781 


14 
14 


9.94069 


0.05 930 


9 


87712 




54 




7 


9.81 796 


9.94095 


0.05 905 


9 


87 701 




53 




8 


9.81 810 


14 


9.94 120 


0.05 879 


9 


87 690 




52 


^p ».. 


9 


9.81 824 


14 


9.94 146 


0.05 854 


9 


87679 




5' 


6 

7 
8 


■'a 

2-5 

3-0 

3-4 
3-8 

4.2 
8.5 

I2.f 


•«5 


10 


9.81 839 


1-+ 
14 
14 
14 
14 
14 
14 
14 
14 
14 
14 
14 
14 
14 


9-94 171 


0.05 823 


9 


87668 




50 


2.5 


II 


9-81853 


9-94197 


0.05 803 


9 


87657 




49 


2.9 
3-3 
3-? 
4-1 

8-3 
12.5 


12 


9.81 868 


9.94222 


0-05 777 


9 


8764? 




48 


9 
10 
20 
30 


13 


9.81 882 
9.81 897 


9-94248 
9-94273 


0.05752 
0.05 726 


9 
9 


87634 
87623 




47 
46 

45 


15 


9.81 911 


9-94299 


0.05 701 


9 


87 612 


i6 


9.819-5 


9-94324 


0.05 67I 


9 


87601 




44 


40 


17.0 


16.6 


17 


981 940 


9.94350 


0.05 650 


9 


87590 




43 


50 


21.2 


20.8 


iS 


9.81 954 


9-94 375 


0.05 625 


9 


87 579 




42 




19 


9.81 069 


9.94400 


0.05 599 


9 


87 568 




41 




i 20 


9.81 983 


9.94426 


0.05 574 


9 


87557 


40 


21 


9.81 997 


9.94451 


0.05 548 


9 


87546 




39 




1 22 


9.82 012 


9-94 477 


0.05 523 


9 


87535 




38 




1 23 


9.S2026 


9-94 502 


0.05 49? 


9 


87 52.3 




37 




24 


9.82 040 


9.94528 


0.05 472 


9 


87512 




36 


1 


25 


9.82055 


9-94 553 


0.05 446 


9 


87 501 


35 


1 26 


9.82 069 


14 


9-94 579 


0.05 421 


9 


87490 


1 1 


34 




14 14 II 


1 27 


9.82083 


14 
I-l 
14 
14 
14 


9.94604 


0.05 395 


9 


87479 




33 


6 


1-4 


1.4 


28 


9.82098 


9.94630 


0.05 370 


9 


87468 




32 


7 


1-7 


1.6 I 


29 


9 82 1 12 


9-94655 


0.05 344 


9 


87457 




31 


8 

9 
10 


1-9 

2 2 

2.4 


1-8 
2.1 

2.3 


30 

31 


9 82 126 

9.82 140 


9.94681 
9-94 706 


0.05 319 
0.05 293 


9 
9 


8744? 
87434 


30 

29 


! 32 


982155 


i 


9-94732 


0.05 268 


9 


87423 




28 


20 


4-8 


4-6 


1 33 


9.83 169 


i-l 


9-94 757 


0.05 243 


9 


87412 




27 


30 


y-2 


7.0 


34 


9.82 183 


14 
14 
14 
14 


9.94782 


0.05 217 


9 


87 401 




26 


40 
50 


12. 1 


9-3 
11.6 


35 


9.82 197 


9. 94 808 


0.05 192 


9 


87389 


25 


36 


9.82 212 


9-94833 


0.05 166 


9 


87 378 




24 




37 


9.82 226 


9.94859 


0.05 141 


9 


87367 




23 




! 38 


9.82 240 


*4 
14 
14 
14 


9.94 S84 


0.05 I \l 


9 


87356 




00 




39 


9.S2 254 


9.94910 


0.05 090 


9 


87345 




21 




40 


9.82 269 


9-94 93§ 


0.05 064 


9 


87333 


20 


41 


9.82 283 


9.94961 


0.05 039 


9 


87322 




19 




42 


9.82297 


14 
14 


9.94986 


0.05 014 


9 


87 311 




18 




43 


9.82311 


9-95011 


0.04 988 


9 


87300 




17 


li II 


44 


9.82325 


14 
14 


9-95037 


0.04 963 
0.04 937 


9 


87288 




16 


6 
7 


I.I 

1-3 


I.I 
1-3 


45 


9-82339 


9.95 062 


9 


87277 


15 


46 


9.82354 


14 


9.95 088 


0.04 912 


9 


87266 




14 


8 


i-^ 


1.4 


47 


9.82368 


i4 
14 
14 
14 


9-95 113 


0.04 886 


9 


87254 




13 


9 


1-7 


1-6 


48 


9.82382 


9-95 139 


0.04 861 


9 


87243 




12 


10 


1.9 


1-8 


! 49 


9-82 396 


9-95 164 


25 
2§ 


0.04 836 


9 


87232 




1 1 


20 
30 


3-8 

S-1 


3-6 

5-5 


! 50 


9.82 410 


9-95 189 


0.04 816 


9 


87 221 


10 


51 


9.82424 


H 


9-95215 


2§ 
25 


0.04785 


9 


87209 




9 


40 


7-6 


7-3 


52 


9-82 438 


14 


9.95 240 


0.04759 


9 


87 198 




8 


50 


9.0 


9.1 


53 


9.82452 


14 


9.95 266 


0.04734 


9 


87187 




7 




1 54 


9.82467 


14 
14 


9.95 291 


23 
25 
2S 
25 
25 
2§ 

25 


0.04 708 


9 


8717? 




6 




55 


9.82 481 


9-95310 


0.04683 


9 


87164 


5 


56 


9.82495 


14 


9-95 342 


0.04658 


9 


87153 




4 




57 


9.82 509 


H 


9-9536? 


0.04632 


9 


87 14T 




3 




5« 


9.82523 


14 


9-95 393 


0.04607 


9 


87130 




2 




59 


9.82 537 


14 
14 


9-95 418 


0.04 581 


9 


87 118 




I 




i 60 


9.82551 


9-95 443 


0.04 556 


9 


8710? 





' 


Log. Cos. 


J_d._ 


Log. Cot. 1 c. (1. 


IaO^. Tan. Lo^. Sin. 


<i. 


/ 


P. P. 



48^ 



69 



42^ 



TABLE IV. 





I 

2 

3 
4 

5 
6 

7 
8 

9 

10 

II 

12 

13 

14 

15 
16 

17 
18 

19 



20 

21 

22 
23 
24 

25 
26 

27 
28 

29 

30 

31 
32 
33 
34 

35 
36 

37 
38 

39 



40 

41 

42 
43 
44 

45 
46 

47 
48 

49 



50 

51 

52 
53 
54 

55 
56 
57 
58 
59 
(JO 



LoGT. Sill. 



9.82551 
9.82 565 
9.82 579 
9.82 593 
9.82 607 



9.82 621 
9.82635 
9.82 649 
9.82 663 
9.82 677 



9.82 691 
9.82 705 
9.82 719 
9-82733 

9 -82 746 
9.82 766 
9.82774 
9.82788 
9.82 S02 
9.82816 



9.82 830 
9.82844 
9.82858 
9.82871 
9.82885 



9.82 899 
9.82913 
9.82 927 
9.82 940 
9.82954 



9.82968 
9.82982 
9.82 996 
9.83009 
9.83023 



9-83037 
9.83051 
9.83 064 

9-83078 
9.83092 



9.83 106 
9-83 119 
983 133 
9-83 147 
9.83 166 



9-83 174 
9.83 188 
9.83 201 
9.83215 
9.83229 



9-83242 
9.83256 
9.83 269 
9-83283 
9-83297 



9.83310 
9-83324 
983337 
9-83351 
9-83365 
9-83 378 

Log. Cos. 



liOff. Tmi. f. (i. I l;o<r. Cot. 




443 
469 

494 
520 

54§ 



824 
850 

87? 
901 
926 



951 
977 
002 
027 
053 



078 
104 
129 

154 
180 



205 
230 
256 
281 
306 



332 
357 
383 
408 

433 



459 
484 
509 

535 
560 



96 



q6 



58? 
611 
636 
661 
687 
712 
737 
763 
788 
813 



839 
864 
889 

915 
946 



9696^ 

liOK. Cot. 



25 
2? 
2? 
2? 
2§ 
25 
2§ 
2§ 
2§ 

25 
2? 



2§ 
25 

25 
25 
2§ 
25 
2? 
2§ 
2! 
25 
2? 
2§ 
2§ 
25 
25 
2§ 
25 
2§ 
2§ 
2§ 
25 
2§ 
25 
2? 
25 
2§ 
2§ 
25 



25 
2§ 

2§ 
25 
2! 
2§ 
2§ 
25 
25 
2! 
25 
25 
2§ 
25 
2§ 
25 
25 

77T. 



0.04 556 
0.04531 
0.04 505 
0.04 480 
0.04454 



0.04 429 
0.04 404 
0.04 378 
0.04353 
0-04 32^ 
0.04 302 
0.04 277 
0.04 251 
0.04 226 
0.04 206 



0.04 175 
0.04 150 
0.04 124 
0.04 099 
0.04 074 



0.04048 
0.04 023 
0.03 997 
0.03 972 
0.03 947 



0.03921 
0.03 896 
0.03871 
0.03 845 
0.03 820 



0.03 795 
0.03 769 
0.03 744 
0.03 718 
0.03693 



0.03 668 
0.03 642 
0.03 617 
0.03 592 
0.03 566 



0.03 541 
0.03 516 
0.03 490 
0.03 465 
0.03 440 



0.03414 
0.03 389 
0.03 364 
003 338 
0-0331 3 
0.03 287 
0.03 262 
0.03 237 
0.03 21 T 
0.03 186 



0.03 161 
0.03 135 
0.03 1 10 
0.03 085 
0-03059 

0-03 034 
Lo^. Tan. 



Loir. Cos. 



9.87 107 
9.87 096 
9.87 084 



87073 
8706: 



87 056 
87039 
87 027 
87 016 
87 004 



86993 
86982 
86 976 
86959 
8694^ 
86 936 
86 924 
86913 
86 901 
86890 



86 878 
86867 
86855 
86844 
86832 



86821 
86. 



86' 
86' 



809 

798 
786 
«6 774 
86763 

86751 
86 740 

9.86728 

9-86 716 



86705 
86 693 
86682 
86 670 
86658 



86 647 
86635 
86623 
86612 
86 600 



86588 
86577 
.^,6 565 

86553 
86542 



86 530 
86518 
86507 

86495 
86483 

86471 
86460 
86448 
86436 
86424 

86412 
Log. Sin. 



00 

59 
58 
57 
56 



55 
54 
53 
52 
_SJ_ 
oO 
49 
48 
47 
46 



24 
23 
2 2 
21 

'9 
18 

17 
16 



15 
14 
13 
12 
1 1 

9 
8 

7 
6 



p. p. 



6 

7 
8 

9 
10 

20 

30 
40 

50 



25 

2.5 
3-0 

3-4 
3-8 
4.2 

8-5 
12.^ 
17.0 
21.2 



25 

2.5 





14 


6 


1.4 


7 


I 


6 


8 


I 


8 


9 


2 


I 


10 





3 


20 


4 


6 


30 


7 





40 


9 


3 


50 


II 


6 



13 

1-3 
1.6 
1.8 
2.0 

2. 2 

4-5 

6.'7 

9.0 

II. 2 



12 II II 



6 


1.2 


I.I 




7 


1-4 


1-3 




8 


1.6 


i.^ 




9 


1.8 


1.7 




10 


2.0 


1-9 




20 


4.0 


.3-8 


3- 


30 


6.0 


s-y 


5- 


40 


8.0 


7-6 


7. 


50 


lO.O 


9-6 


9- 



47° 



p. p. 



70 



TABLE IV. 



43' 



10 

II 

12 



15 
i6 

i8 

19 



20 

21 

22 
23 
24 

25 
26 

27 
28 

29 

30 

31 

32 

33 
34 

35 
36 
37 
38 
39 



40 

41 

42 
43 
44 

45 
46 

47 
48 

49 
50 

51 

52 
53 

54 

55 
56 
57 
58 
59 
(JO 



1,0^'. Sill 



9-83 378 
9-83 392 
9.83405 
9.83419 
983432 



9.83446 
9-83459 
9-83473 
9-83486 
9.83 500 



9-83513 
9.83 527 
9.83 540 

9-83 554 
9.83 567 



9.83 586 

9-83 594 
9.83607 
9.83 621 
9-8363-4 



9.83647 
9.83661 
9.83674 
9.83688 
9.83701 



9-83714 
9-83728 
9.83741 

9-83754 
9.83768 



9-83781 
9-83794 
9.83808 
9.83821 
9 83 834 



9.83847 
9.83 86 1 

9.83874 
9.83887 
9.83906 



9.83914 

9-83927 
9.83946 

9-83953 
9.83967 



9.83 980 

983993 

9.84 oog 
9.84019 
9-84033 



9. 84 046 
9.84059 
9.84072 
9.84085 
9.84098 



9.84 in 
9.84124 
9.84138 
9.84 151 
9.84 164 

9-84177 

Log. Cos. I d. 



Lo|f. 'I'liii. c. il. Lor. Cot. 



9.96965 
9.96991 
9.97 016 

9-97 041 
9.97067 



9.97092 
9-97 II? 
9-97 143 
9.97 168 

9-97 193 



9-97 219 
9-97 244 
9-97 269 
9-97 295 
9.97 320 



9-97 34§ 
9-97 370 
9-97396 
9-97 421 
9-97 446 



9.97472 

9-97 49? 
9-97 522 
9,97 548 

9-97 573 



9-97 598 
9.97624 

9-97649 
9.97674 
9.97699 



9.97725 
9-97 750 
9-97 77 § 
9.97 80 r 
9.97 826 



9.97851 

9-97877 
9.97902 

9-9792? 
9.97 952 



-3 

2§ 

25 

2? 
2! 
25 
2§ 
25 
25 
2§ 
25 
25 
25 
2! 
2§ 
25 
25 
25 
25 
25 
2§ 
2§ 
25 
2$ 
25 
25 
25 
2§ 

2S 
25 
2S 
25 
2§ 
25 
Log:. Cot. | c. d. 



9-97 978 
9.98 003 
9.98028 
9.98054 
9.98079 



9.98 104 
9.98 129 

9-98155 
9.98 186 
9.98 205 



9.98 231 
9.98 256 
9.98281 
9.98 306 
9-98 332 



9-98 35? 
9.98382 
9.98 408 
998433 
9-984 58 
9.98483 



25 

2§ 
25 
25 
25 
2§ 
25 
25 
2§ 
25 
25 
2§ 
25 
25 
25 
25 
2§ 
25 
2§ 
25 
25 



0.03034 
0.03 009 
0.02 984 

0.02 958 
0.02 933 



0.02 908 
0.02 882 
0.02 857 
0.02 832 
0.02 805 



0.02 781 
0.02 756 
0.02 736 
0.02 705 
0.02 680 



0.02 654 
0.02 629 
0.02 604 
0.02 578 
0.02 553 



0.02 528 
0.02 502 
0.02 47? 
0.02 452 
0.02 427 



0.02 401 
0.02 376 
0.02 351 
0.02 325 
0.02 ^06 



0.02 275 
0.02 249 
0.02 224 
0.02 199 
0.02 174 

0.02 148 
0.02 123 
0.02 098 
0.02 072 
0.02 04? 



0.02 022 
o.oi 996 
o.oi 971 
0.0 1 946 
o.oi 921 



O.OI 895 
O.OI 876 
O.OI 845 
O.OI 819 
O.OI 794 



0,01 769 
O.OI 744 
O.OI 718 
O.OI 693 
O.OI 668 
O.OI 642 
O.OI 61? 
O.OI 592 
O.OI 567 
O.OI 541 

o-oi 516 

Log. Tan. 



Loc Cos. 



86 412 
86 401 
86389 

86377 
86365 

86354 
86 342 
86 330 
86318 
^^ 3?6 
86 294 
86282 
86 271 
86259 
86247 



86235 
86223 
86 21 1 
86 199 
86 1 8? 



86176 
86 164 
86152 
86 140 
86128 



86 116 
86 104 
86092 
86080 
86068 



86056 

86044 
86032 
86 020 
86008 



85996 
85984 
85972 
85 960 
85948 



85936 
85924 
85912 
85 900 
8588? 

85"87l 
85863 
85851 

85839 
85827 



85815 
85803 
85791 
85778 
85766 



85754 
85742 

85730 

85718 

85 7og 

9.85693 



Log. Sin. 



(10 

59 
58 
57 
J^ 
55 
54 
53 
52 
5' 
50 
49 
48 
47 

45 
44 
43 
42 
41 
40 
39 
38 
37 
_3i 
35 
34 
33 
32 
31 
30 

29 
28 

27 
26 



25 

24 

23 
22 
21 

'20 

19 
18 

17 
16 



15 
14 
13 
12 
II 

To 

9 

8 

7 
6 





2S 


25 


6 


2-§ 


2. 


7 


3-0 


2. 


8 


3-4 


3. 


9 


3-8 


3- 


10 


4.2 


4- 


20 


8.S 


8. 


30 


12.? 


12. 


40 


17.0 


16. 


50 


21.2 


20. 



6 

7 
8 

9 
10 

20 
30 
40 

50 



13 


13 


1-3 
1.6 
1.8 




2.0 




2.2 


2 


4-5 

6.7 

9-0 

II. 2 


4- 

6. 

8. 

10. 





12 


12 


I] 


6 


1.2 


1.2 




7 


1-4 


1-4 




8 


1-6 


1.6 




9 


1-9 


1.8 




10 


2.1 


2.0 




20 


4-1 


4.0 


3- 


30 


6.2 


6.0 


5- 


40 


8.3 


8.0 


7- 


50 


10.4 


lO.O 


9. 



46^ 



p. p. 



71 



44= 



TABLE IV. 



10 

II 

12 

13 

14 



15 
i6 

17 
i8 

19 



20 

21 
22 
23 
24 

25 

26 
27 
28 



30 

31 
32 

33 

34 

35 
36 
37 
38 
39 



40 

41 

42 
43 
44 



45 
46 

47 
48 
49 
50 
51 
52 
53 
54 

55 
56 
57 
58 
59 
60 



TiOi?. Sill. 



9.84177 
9.84 190 
9.84203 

9-84216 
9.84 229 



9.84242 
9.84255 
9-84268 
9.84281 
9.84294 



9.8430? 
9.84 320 
9-84333 

9-84 346 
9-84359 



9-84372 
9-84385 
9-84 398 
9. 84 4 1 1 
9.84424 



984437 
9.84450 
9.84463 
9.84476 
9.84489 



9.84502 
9.84514 

9-8452? 
9.84540 

984553 



9.84 566 
9.84579 

9-84592 
9. 84 604 
9.8461? 



9.84636 
9.84643 
9.84656 
9.84669 
9.84681 



9.84694 
9.84707 
9.84720 
9.84732 
9-8474! 



9-84758 
9.84771 

9-84783 
9-84796 
9.84 809 



9.84822 

9-84834 
9.84847 
9.84860 
9.84872 



9.84885 
9.84898 
9.84 910 
9.84923 
9-84936 

9-84 948 
Log. Cos. 



13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
12 
13 
13 
13 
13 

13 
12 

13 
13 
13 
12 

13 
13 
12 

13 

13 

12 

13 
13 
12 

13 
12 

13 
12 

13 
12 

13 
12 

13 
12 

13 
12 
12 

13 
12 

12 

13 
12 
12 
13 
12 



Log. Tan. c. d 



9.98483 
9.98 509 
9-98 534 
9-98 559 
9.98 585 



9.98 610 
9-9863? 
9. 98 660 
9.98686 
9-98711 



9-98736 
9.98 762 

9-98787 
9.98812 

9-9883? 



9.98863 
9.98888 
9.98913 

9-98 938 
9.98964 



9-98989 
9.99014 
9.99040 
9.99065 
9.99096 



9.9911! 
9.99 141 
9.99 166 
9.99 191 
9-99 216 



9.99 242 
9-99267 
9.99 292 
9.99318 
9.99343 



9-99368 
9-99 393 
9.99419 
9.99444 
9.99469 



9-99 494 
9-99 520 
9-99 545 
9-99 570 
9-99 59§ 



9.99 621 
9.99646 
9-99671 
9.99697 
9.99722 



9-99 747 
9-99772 
9.99798 
9.99823 
9-99848 



9-99873 
9.99 899 

9-99924 
9.99949 

9-99 974 
0.00000 
ToiTcoitr 



25 

25 
25 

2S 
25 
25 
25 
2S 
25 
2§ 
25 
25 
2S 
25 
2? 
25 
2§ 
25 
2§ 
2? 
25 
2S 
25 
25 

25 

2§ 
25 
2? 
25 
25 
25 
25 
25 
25 
25 
25 
2§ 
25 
25 

25 
2! 
25 
25 
25 
25 
25 
25 
2§ 
25 
2§ 
25 
25 
25 
25 
25 
2§ 
25 
2? 
25 
2§ 
c7d7 



Log. Cot. 



o.oi 516 
o.oi 491 
0.01 465 
O.OI 446 
O.OI 415 



O.OI 390 
O.OI 364 
O.OI 339 
O.OI 314 
O.OI 289 



O.OI 263 
O.OI 238 
O.OI 213 
O.OI 18? 
O.OI 162 



O.OI 137 

O.OI 112 

O.OI 085 
O.OI 061 
O.OI 036 



O.OI 010 
0.00 985 
0.00 960 
0.00 935 
0.00 909 



Log. Cos. 



9.85693 
9.85681 

9.85 669 

9.85657 
9-85644 



9.85632 

9.85 620 
9.85 608 

9-85 59§ 
9.85 583 



9.85571 
985559 
9-85 546 
9-85 534 
9.85 522 



9.85 509 
9.8549? 
9.85485 
9.85472 
9.85 466 



0.00 884 
0.00 859 
0.00 834 
0.00 808 
0.00 783 



0.00758 
0.00733 
0.00 70? 
0.00 682 
0.00 657 



0.00 631 
0.00 605 
0.00 581 
0.00 556 
0.00 536 



0.00 5o§ 
0.00 480 
0.00 455 
0.00429 
0.00 404 



0.00379 
0.00353 
0.00328 
0.00 303 
0.00 278 



0.00 252 
0.00 22? 
0.00 202 
0.00 177 
0.00 15T 



0.00 126 
0.00 lOI 
0.00076 
0.00056 

0.00 02§ 
0.00000 
J^Og. Tan. 



9.85448 

9-85435 
9.85423 
9.854II 

9-85 398 



9.85 386 

9-85374 
9.85361 

9-85 349 
9-85 336 



9.85324 
9.85312 
9.85 299 
9.85 287 
9-85 274 
9.85 262 
9.85249 
9.85 237 
9.85 224 
9.85 212 



9.85 199 
9.85 187 
9.85 174 
9.85 162 
9.85 149 



9-85 137 
9.85 124 
9.85 112 
9.85099 
9.85087 



9.85074 
9.85 062 
9.85049 
9.85037 
9.85 024 



9.85 oil 

9-84999 
9.84986 
9.84974 
9.84 961 

9-84948 

Log. Sill. 



GO 

59 
58 
57 
56 



55 
54 
53 
52 
51 



50 

49 
48 

47 
46 



45 
44 
43 
42 
41 



40 

39 
38 
37 
36 



35 
34 
33 
32 
31 



30 

29 
28 

27 
26 



25 
24 

23 
22 
21 



20 

19 
18 

17 
16 



15 
14 
13 
12 
II 



10 

9 
8 

7 
6 





s.'J 


2-1 


6 


2.§ 


2. 


7 


3-0 


2. 


8 


3-4 


3. 


9 


3.8 


3. 


10 


4.2 


4. 


20 


8.5 


8. 


30 


12.? 


12. 


40 


17.0 


16. 


50 


21.2 


20. 



\6 

! 7 
8 

9 
10 

20 

30 
40 

50 



13 

1-3 
1.6 
1.8 
2.0 

2.2 

4-5 

6.? 

9.0 

11.2 



13 

1-3 
1-5 
1-7 
1-9 

2.1 

4.3 
6.5 

8.6 
10.8 





12 


6 


1.2 


7 


1.4 


8 


1-6 


9 


1.9 


10 


2.1 


20 


4.f 


30 


6.2 


40 


8.3 


50 


10.4 



12 

;l.2 
1.4 
1.6 
1.8 
2.0 
4.0 
6.0 
8.0 

lO.O 



45° 



p. p. 



72 



TABLE V. 



Natural Sines, Tangents, Co- 
tangents AND Cosines. 













0" 


-10^ 










TABLE V. 


6 / 


Sin. 


1 ^■ 


Tan. 


d. 


Cot. 


d. 


Cos. 


d. 




p. p. 





0.0000 




0.0000 




00 




1. 0000 




90 




lO 


0.0029 




0.0029 


2y 
29 


343-773 




1.0000 





50 




20 


0.0058 




0.0058 


171.885 




I. 0000 




40 




30 


0.008^ 


29 


0.0087 


29 


114.588 




0.9999 




30 




40 


O.OII5 


O.OII6 




85.9398 




0.9999 




20 




50 

1 


0.0145 


29 


0.0145 
0.0174 


29 
29 


68.7501 
57.2899 




0.9999 





10 
89 


■^o 26 20 


0.0174 


0-9998 


10 


0.0203 




0.0203 


29 


49.1039 


6.1398 


0.9998 


° 


50 


I 


3.0 2 


9 2.9 


20 


0.0232 




0.0233 




42.9641 


0-9997 




40 


3 


6.0 5 

9.0 8 


9 5-8 
s 8 7 


30 


0.0262 




0.0262 




38.1884 




0.9996 




30 


8 11.6 


40 


0.0291 




0.0291 




34-367? 


3.1261 
2.6053 

2 . 2046 
1-8898 


0. 9996 




20 


5 


15.0 14 


7 '4-5 


1 50 

2 

10 


0.0320 


29 
29 
29 


0.0320 


2y 

29 
29 


31.2416 


0.9995 




10 
88 

50 


6 

7 
8 

9 


18.0 17 

21.0 20 
24.023 
27.0 26 


7 17-4 

6 20-3 
6 23.2 
5 26.1 


0.0349 


0.0349 


28.6362 


0.9994 


0.0378 


0.0378 


26.4316 


0.9993 


20 
30 


0.0407 
0.0436 


29 


0. o4of 
0.0436 


29 


24.541? 
22.903? 


I . 6380 


0.9991 
0. 9996 




40 
30 




40 


0.0465 


29 


0.0466 


2y 


21.4704 


>-4333 


0.9989 




20 




50 
3 

10 


0.0494 


■2y 
29 
29 


0.0495 


29 
29 
29 


20.2055 
19.0811 


1.2648 
I. 1244 
1.0061 


0.9988 




10 

87 
50 




0.0523 


0.0524 


0.9986 


0.0552 


0-0553 


18.0750 


0.9984 


20 


O.058T 




0.0582 




17.1693 




0.9983 




40 


28 5 4 4 


30 


0.0610 




0.061 1 




16.3498 




0.9981 




30 


I 


2.8 0-5 


0.40.4 


40 


0.0639 


2y 


0.0641 


2y 


15.6048 


7450 


0-9979 


2 


20 


3 


5.7 I.O 
8-5 1-5 


1.3 1.2 


50 
10 


0.0663 


29 
29 


0.0670 


^9 
29 
29 


14.9244 
14-3006 

13-726? 


6237 
5739 


0.997? 


2 
2 
2 


10 
86 

50 


4 

5 

6 


11.4 2.0 
14.22.5 
[7.1 3.0 


1.8 1.6 

2.2 2.0 
2.72.4 


0.0697 


0.0699 


09975 


0.0726 


0.0728 


0-9973 


20 


0.0755 




0.0758 




13.1969 




0.9971 




40 


7 

R 


'9-9 3-5 
22.8 4.0 


3.6 3.2 


30 


0.0784 




0.0787 




12.7062 




0.9969 




30 


9 


25-6 4-5 


4.5 3-6 


, 40 


0.0813 


29 


0.0816 


2y 


12.2505 


4557 


0.9967 


2 


20 




50 
6 


0.0842 


29 
29 


0.0845 


2y 
29 


1 1.826T 


4243 
3961 
3706 
3475 


0.9964 


5 


10 
85 




0.0871 


0.0875 


11.4306 


0.9962 


10 


0.0900 


29 


0.0904 


2Q 


11.0594 


0.9959 


3 


50 




20 


0.0929 


29 


0.0933 


29 


10.7119 


3265 


0-9956 




40 




30 


0.0958 


29 
29 
29 

29 


0.0963 




10.3854 




0.9954 




30 




40 

i G 

10 


0.0987 

O.IOlg 


0.0992 
0. 1021 


29 
29 
29 
29 


10.0786 
9.788T 


2899 
2738 
2590 
2454 


0.9951 
0.9948 


3 
3 
3 
3 
3 


20 
10 
84 

50 


1 < 

2 c 

3 
4 


3 3 

'-30.3 c 

3.7 0.6 c 
.0 0.9 c 

.4 1.2 I 


2 2 

.2 0.2 
.50-4 
.7 0.6 

.00.8 


0.1045 


0.1051 


9.5143 


0.9945 


0.1074 


■0.1086 


9-2553 


0.9942 


1 20 


O.I 103 


29 


0.1 1 10 




9.0098 




0.9939 




40 


6- 


>.i 1.8 I 


.5 1.2 


i 30 


O.I 1 32 




0.1139 




8.7769 


22x3 

2106 

2006 

1913 
1825 


0-9935 




30 


7 '■ 


.42.1 1 


.7 1-4 


40 

50 

7 

10 


0.II6I 
O.I 190 


29 

29 
29 


0. 1169 
O.II98 


29 
29 
29 

29 


8-5555 
8.3449 


0-9932 
0.9929 


3 
3 
3 


20 
10 
83 

50 


8; 
9. 


.8 2.42 
j.i 2.72 


.0 1.6 
.2 1.8 


0.I2I8 


0.1228 


8.1443 


0.9925 




0.124^ 


0.1257 


7-9530 


0.9922 


20 
30 


O.I276 
0.1305 


29 
2§ 


0.1287 
0.1316 


29 
29 


7.7703 
7-595? 


1746 
1670 


0. 99 1 8 
0.9914 


3 


40 
30 




' 40 


0.1334 


0.1346 


7.4287 


0.9910 




20 




1 50 

8 

10 


0-1363 


28 
29 


0.1376 


29 
29 
30 


7.268? 
7- 1 153 


1599 
1534 
1471 


0.9906 


4 
4 
4 


10 

82 
50 


1} , R 


0.I39I 


0.1405 

0.1435 


0.9902 




1 o.i 0.] 

2 0.3 0.5 


0.0 
0. 1 


0.1426 


6.9682 


0.9898 


20 


0.1449 




0.1465 


6.8269 


1358 
1306 


0.9894 




40 




30.40.: 


O.I 


30 


0.1478 




0.1494 




6.6911 


0. 9890 


4 


30 




i 0.6 0.4 


0.2 


40 


0.1507 




0.1524 




6.5605 


0.9886 




20 




Sh.go.t 


0.3 


50 

9 

10 


0.1535 


28 

29 

28 


0.1554 


29 
30 

29 


6-4348 


1257 
1211 

1167 


0.988T 


4 
4 
4 


10 
81 

50 




7 1.0 0.5 
3 1.2 0.1 


0.3 
0.4 
0.4 


0.1564 


0.1584 


6.313^ 


0.9877 

0.9872 


0.1593 


0.1613 


6.1976 




20 

30 


0.1622 
0.1656 


28 


0.1643 
0.1673 


30 


6.0844 
5-975? 


1087 


0.986? 
0.9863 


4 


40 
30 




40 


0.1679 




0.1703 




5.8708 




0.9858 


b 


20 




50 
10 


0.1708 


-iy 

28 


0.1733 


30 


5-7693 


980 


0-9853 


5 
5 


10 
80 




0.1736 


0.1763 


5-6713 


0.9848 




Cos. 


J*^ 


Cot. 


d. 


Tan. 


d. 


Sin. 


d. 


/ 


P. P. 



80°-90 



74 



1 0°-20^ 



TAHLF, V 



o / 


Sin. 


d. 


Tan. 


d. 


Cot. 


d. 


Con. 


d. 


1'. 1'. 


10 

lO 


O.173S 


28 


0.1763 

0.1793 


30 


56713 


949 


0.9848 

0.9843 


80 




0.1765 


5-5764 


5 


50 


20 


0.1793 


28 


0.1823 


i" 


5.4845 


890 
862 

836 
811 
787 
764 

742 


0.9838 


5 


40 


1 


30 

40 

50 

11 

10 


0.1822 
O.1851 
0. 1879 


29 

28 
28 
28 
28 


0.1853 
0.1883 
O.I9I3 


3° 
30 
30 
30 
30 


S-39SS 
5-3093 
5-2256 


0.9832 
0.9827 
0.9822 


5 
5 
5 
5 
6 


30 
20 
10 
79 

50 


33 

' 3-3 

2 6.6 

3 9-9 


32 31 i 

3-2 31 

6.4 6.2 

9.6 9.3 


0.1908 

o«936 


0.1944 


S-M4S 


O.981S 


0.1974 


5.0658 


0.9816 


20 


0.1965 


^i 


0. 2004 


30 


4.9894 


0.9805 


6 


40 


4 »3.2 

5 »6.s 


12.8 12.4 
16.0 15.5 


30 


0.1993 




0. 2034 




4.9151 


721 


0.9799 




30 


6 19.8 


19.2 18.6 


40 
50 

12 

10 


0.2022 
0.2056 


28 
28 
28 


0.2065 
0.2095 


30 
30 
3° 
30 


4.8430 
4-7728 
47046 


701 
682 

664 
646 


0.9793 
0.978? 


6 
6 
6 


20 
10 

78 
50 


7 23.' 
826.4 
9 29.7 


22.4 21 .7 

25.624.8 
28.827.9 \ 


0.2079 


0.2I2§ 


0.9781 


0.210^ 


0.2156 


4-6383 


0.9775 


1 


20 


0.2136 




0. 2 1 85 


4.573S 




0.9769 


6 


40 




30 


0. 2 1 64 




0.2217 




4.5107 


613 


0.9763 


6 


30 


36 30 29 


40 


0.2193 




0.224? 




4-4494 




0-9756 


20 


I 3.5 


3.0 2.9 


50 
13 

10 

20 


0.222 1 


28 
28 

28 


0.2278 


3" 
30 

31 
30 


4.3897 


597 
582 
568 
553 
540 
527 
515 
502 
491 
480 
469 


0.9750 
09743 


b 
6 

6 
6 


10 
77 

50 
40 


2 6,1 

3 9-1 

4 12.2 

5 15-2 

6 18.3 


6.0 5.8 
9.0 8.7 

12.0 II. 6 
15.0 14.5 
i8.o 17.4 


0.2249 


O.23O8 


43315 

4-2747 
4-2193 


0.2278 
0.2306 


0.2339 
0.2370 


0.9737 
0.9730 


30 
40 


0.2334 
0.2362 


28 

28 


0.2401 
O.243T 


31 
3° 


4-1653 
4.1125 


0.9723 
0.9717 


6 


30 
20 


7 21.3 
824.4 


21.0 20.3 
24.0 23.2 


50 
14 

10 


0.2391 


28 

28 

28 


0. 2462 


31 

30 


4.0616 


0.9710 


7 

7 


10 
76 

50 


9 27-4 


27.0 26.1 \ 


0.2419 


0.2493 


4.0108 


0.9703 




0.2447 


0.2524 


3-9616 


0. 9696 


20 


0.247I 


0.2555 


31 


3-9136 


0.9688 




40 


28 28 2*7 


30 


0.2504 


-=8 


0.2586 


31 


3.8667 


0.9681 


7 


30 


I 2.8 


2.8i 2.7 


40 


0.2532 




0.2617 


31 


3.8208 


458 


0.9674 


1 


20 


2 5.7 


5-6 5-4 


SO 


0.2560 


28 


0. 2648 


31 


3-7759 


449 


0.9665 


1 


10 


3 8.5 


8.4 8.1 


15 

10 


0.2588 


28 

28 


0.2679 


31 


3.7326 


429 


0.9659 


8 


75 

50 


4 ".4 

5 14-2 

6 17. 1 


II. 2 10.8 i 
I4-OI3.5 
16.8 16.2 


0.2616 


0.2716 


3.6891 


0.9651 


20 


0.2644 


28 


0.2742 




3-6470 




0.9644 




40 


. 


j 


30 


0.2672 


08 


0.2773 




3-6059 


403 


0.9636 


8 


30 


822.8 


22.4 21.6 1 


40 


0.2700 


28 


0.2804 




3-5655 




0.9628 


8 


20 


925.6 


25.224.3 


50 
16 

10 


0.2728 


28 
28 
78 


0.2836 


31 
31 


3-5261 


387 
379 
371 


0.9626 


8 
8 
8 


10 
74 

50 


10 Q 8 


0.275S 


0.2867 


3-4874 


0.9612 


0.2784 


0.2899 


3-4495 


0. 9604 


20 


0.2812 




0.2930 




3-4123 


364 

357 


0-9596 


8 
8 


40 


I I.O 


0.90.8 


30 
40 


0.2840 
0.2868 


28 


0.2962 
0.2994 


32 


3-3759 
3-3402 


0.9588 
0.9580 


30 
20 


2 2.0 

3 3-° 


1.8 1.6 
2.72.4 


50 
17 

10 


0.2S96 


27 
28 


0.3025 


31 
32 
31 


3-3052 


343 
337 


0.9571 


8 
8 


10 
73 

50 


4 4.0 

5 50 
66.0 


3-6 3-2 
4.54.0 
5.44.8 


2923 


0-3057 


327o§ 


0.9563 


0.2951 


0.3089 


3-2371 


0.9554 


20 


0.2979 




0. 3 1 2 1 


32 


3. 2040 


331 


0.9546 


8 


40 


7 7-0 

8 8.0 


6.35.6 
7.2 6.4 


30 


0. 3007 


^1 


0-3153 


32 


3-1716 


324 


0.9537 




30 


99.0 


8.17.2 


40 


0.303s 




0.3185 


32 


3-1397 


319 


0.9528 


8 


20 




so 


0.3062 


27 


0.3217 


J'-i 


3.1084 


313 


0.9519 


y 
9 


10 




18 


0.3090 




0.3249 


32 


3-0777 




0.9516 


72 


fi fj f. ^ 


10 


0.3118 
0.314! 


27 


0.3281 


32 
32 


3-0475 


296 


0.9501 





50 


7 

I 0.70 


7 0.6 0.5 


20 




0.3313 




3-OI78 




0.9492 




40 


2 1.5 I 


4 1.2 1.0 


30 
40 


0.3173 
0.3206 


27 


0.3346 

0.3378 


32 
32 


2.9887 
2.9606 


291 
286 


0.9483 
0.9474 


9 
9 


30 
20 


3 2.2 2 

4 3.02 


I 1.8 1.5 
82.42.0 , 


50 
19 

10 


3228 
0.3255 


27 
27 
27 

27 


0.341 1 


32 
32 
32 
32 


2.9319 


277 
272 
267 


0.9464 


y 
9 
9 
3 


10 
71 

50 


53.73 
64.54 

7 5-2 4 

8 6.0 5 


5 3.0 2. s j 
2 3.6 3.0 j 

) 

9 4. 23s 


0.3443 


2.9042 


0.9455 


03283 


0.3476 


2.8770 


0.9445 


20 


0.3310 




0-3S08 




2.8502 


263 


0.9436 


9 


40 


96.716 


35.44.5 1 


30 


0-3338 




0.3541 




2.8239 


259 


0.9426 




30 


i 


40 


0-3365 




0-3S74 




2.7980 


0.9416 


. 


20 


1 


SO 
20 


0-3393 


■'J 
27 


0. 3607 


33 
32 


2.7725 


254 
250 


0.9407 


9 
10 


10 
70 


i 


0.3420 


0.3639 


2-7475 


0.9397 




Cos. 


d. 


Cot. 


d. Tan. I 


d. 


Sin. 1 


d. 


/ 


P. P. 






^^^ 





















70°-80 



75 



20°-30^ 



TABLE V. 



20 

lO 

20 
30 
40 
50 

21 
10 
20 

30 

I 40 

50 

22 

10 
20 

30 
40 

50 

23 

10 
20 

30 
40 

50 

24 

10 
20 

30 

40 

50 

25 

10 
20 

30 
40 

50 

26 

10 

20 

30 
40 

50 

27 

10 
20 

30 
40 

50 

28 
10 
20 

30 

I 40 

50 

29 

10 

20 

30 
40 

50 

30 



Sin. 

o 3420 



0.3447 
0.3475 
0.3502 
0.3529 

0.355S 



03583. 

0.361 1 
0.3638 
0.3665 
0.3692 
0.3719 



03746 



0.3773 
o. 3800 
0.3827 

0.3853 
o. -,880 



0.3907 



0.3934 
0.3961 
0.3987 
0.4014 
0.4041 



0.406^ 



0.4094 
0.4120 
0.4147 

0.4173 
0.4200 



o 4226 



0.4252 
0.4279 
0.4305 
0.4331 
0.435^ 



04383 



0.4410 

0.4436 

0.4462 

0.4488 
0.4514 



04540 



0.4566 

0.4591 

0.461^ 

0.4643 

0.4669 



0.4694 



0.4720 

0.4746 

0.4771 
0.4797 

0.4822 



0.4848 



0.4873 

0.4899 

0.4924 
0.4949 
0.4975 



0.5000 

Cos. 



Tan. 

_a3639 

0.3672 
0.3705 

0.3739 
0.3772 
0.3805 



0.3838 

0.3872 

0.3905 

0.3939 
0.3972 

0.4006 



0.4040 



0.4074 
0.4108 
0.4142 
0.4176 
0.4216 



0.4244 



0.4279 

0.4313 
0.4348 

0.4383 
0.441^ 



04452 



0.4487 
0.4522 

0.4557 
0.4592 
0.462^ 



0.4663 



0.4698 
0.4734 
0.4770 
0.4805 
0.484T 



0.487^ 



0.4913 
0.4949 
0.4986 
0.5022 
0.5058 



05095 



0.5132 
0.5169 
0.5205 
0.5242 
0.5280 



05317 



0.5354 
0.5392 
0.5429 
0.546? 
0.5505 



0-5543 



0.5581 
0.5619 
0.5657 
o. 5696 
0.5735 



0.5773 
Cot. 



Cot. 

2-7475 




2.5826 
2. 5604 

2.5386 
2.517T 
2.4959 



24751 



2.4545 
2.4342 
2.4142 

2-3945 
2.3750 



23558 

2.3369 
2.3182 
2.2998 
2.2815 
2.263^ 



2.2460 



2.2285 
2.2113 
2.1943 
2.1775 
2. 1609 



2.1445 



2.1283 
2. 1 1 23 
2.0965 
2.0809 
2.0655 



2.0503 



2.0352 

2.0204 

2.0057 

991 1 

9768 



.9626 



.9486 

•9347 
.9210 
.9074 
.8940 



.8807 

.8676 
.8546 
.841? 
.8290 
.8165 



.8046 



.7917 

-7795 
.7675 

•7555 
.743? 



I -7320 

Tan. 



247 
242 
239 
235 
232 
228 
225 

221 
218 

212 
2og 
206 
203 
200 
197 
194 
192 
189 
187 



179 

17s 
172 
1 70 
168 
166 
164 
162 

IS4 
152 
150 
'48 
147 
145 
143 
142 
140 
139 
137 
136 
134 
132 

131 

130 

I2§ 
127 
125 
124 
123 
122 
120 
119 
118 



Cos. 

09397 

0.9387 
0.9377 
0.9366 

0.9356 
0.9346 



0.9336 



0.9325 

0.9315 
0.9304 
0.9293 
0.9282 



0.9272 



0.9261 
0.9250 
0.9239 
0.922^ 
0.9216 



0.9205 



0.9193 
0.9182 
0.9176 
0.9159 
0.9147 



0-9135 



0.9123 
0.9111 
o. 9099 
0.9087 
0.9075 



0.9063 



0.9050 
0.9038 
0.9026 
0.9013 
0.9006 



0.8988 



0.8975 
0.8962 
o. 8949 

0.8936 
08923 



0.8910 



0.8897 
0.8883 
0.8870 
0.8856 
0.8843 



0.8829 



0.8816 
0.8802 
0.8788 
0.8774 

0.8766 



0.8746 



0.8732 

0.8718 

0.8703 

0.8689 
0.8675 

0.8666 

Sin. 



d. 



70 

50 
40 

30 
20 
10 
69 

50 
40 
30 
20 
10 

68 
50 
40 
30 
20 
10 

67 
50 
40 
30 
20 
10 

66 
50 
40 
30 
20 
10 

65 

50 
40 
30 
20 
10 

64 
50 
40 
30 
20 
10 

63 
50 
40 
30 
20 
10 

62 
50 
40 
30 
20 
10 

61 
50 
40 
30 
20 
10 

60 



39 38 37 36 



I 


3-9 


3-8 


3-7 


3.6 


2 


7-» 


7.6 


7.4 


7.2 


3 


11.7 


II. 4 


10. 1 


10.8 


4 


.5-6 


15.2 


.4.8 


14.4 


5 


19-5 


19.0 


18.5 


18.0 


6 


23-4 


22.8 


22.2 


21.6 


7 


273 


26.6 


2:5.9 


25.2 


8 


31.2 


30.4 


29.6 


28.8 


9 


35-1 


34-2 


33-3 


32.4 



35 35 34 33 



3-5 
7-1 

[O.g 

4114.2 

5|i7-7 
6,21.3 



7l24-8|24-5 
8|28. 428.0 

931-9131-5 



3.4 3-3 
6.8 6.6 
10.2 9.9 

13.6 13. 2 
17.0 16.5 
20.4, 19.8 

23.8 23.1 
27.2 26.4 
30.6 29.7 



2f 27 26 25 



I 


2.7 


2.7 


2.6 


2.5 


2 

3 


5-5 
8.2 


5-4 
8.1 


5.2 

7-8 


5.0 
7-5 


4 


II. 


10.8 


10.4 


10. 


5 
6 


137 
16.5 


13-5 
16.2 


13.0 
15-6 


12.5 
15.0 


7 


19.2 


18.9 


18.2 


I7.S 


8 


22.0 


21.6 


20.8 


20.0 


9 


24.7 


24- 3 


23-4 


22.5 


14 14 13 12 


I 


1.4 


1-4 


'•3 


1.2 


2 


2.9 


2.8 


2.6 


2.4 


3 


4-3 


4-2 


3-9 


3-6 


4 


5-8 


5.6 


5-2 


4.8 


5 
6 


7.2 
8.7 


7.0 

8.4 


6.5 
7.8 


6.0 

7-2 


7 


10. i 


9.8 


g.i 


8.4 


8 


II. b 


II. 2 


10.4 


9.6 


9 


13.0 


12.6 


II. 7 


10.8 



II II 10 



i.i 


1. 1 


I . 


2-3 


2.2 


2. 


3-4 


3-3 


3- 


4.6 


4-4 


4- 


5-7 
6.9 


5-5 
6.6 


5- 
6. 


8.0 
9.2 


7-7 

8.8 


7 

8 


10.3 


9-9 


9- 



P. p. 



60-70 



76 



TABLE V. 



30°-40^ 



i ° ' 


Siu. 


d. 


Tail. 


(1. 


Cot. 


(1. 


Cos. 


(1. 




1'. r. 




30 


0.5000 




0.5773 


1.7320 




0.8666 




00 






lO 


0.5025 


-5 


0.5812 


3y 


1.7204 




0.8645 


'■' 


50 






20 


0.5050 




0.585T 




1.7090 




0.8631 




40 


49 49 48 47 46 




30 


0.5075 


-5 


0.5896 




1.6976 




0.8616 




30 


I 


4y 


4 


y 4- 


B 4- 


7 4-6 




40 


0.5100 


^■i 


0. 5929 


39 


1.6864 


112 


0.8601 


'5 


20 


2 
3 ' 


y-9 


9- 
14. 


H 9. 
7 lii. 


U 9. 


♦ 9-2 

I 13.8 




50 
31 

10 


0.5125 


25 


0. 5969 


39 
39 
40 


1.6753 


no 

109 
108 
107 


0.8586 
0.8575 


15 


10 
59 

50 


419-8 
524.7 
629.7 


ig.6 19.2 18. 
24.524.023. 
29.438.828. 


318.4 
523-° 

2 27.6 




0.5156 


O.60O8 


1.6643 




0.5175 


0.6048 


1-6533 


0.8556 




20 
30 


0.5200 
0.5225 


25 


0.6088 
0.6128 


40 


1.6425 
1.63I8 


0.8541 
0.8526 


15 


40 
30 


7 34-6 

8 39-6 


34- 
39- 


333- 
2,38. 


5 32.9 32.2 
437.6,36.8 




40 


0.5250 


-'.S 


0.6168 


40 


1. 6212 


106 


0.8511 


ib 


20 


9 44-5 


44- 


1I43- 


2|42. 


3l4i-4 




50 
32 

10 


0.5274 


24 
24 

25 


O.6208 


40 
40 
40 


1. 610? 
1.6003 


104 
103 


0. 8496 
0.8480 


IS 

15 


10 
58 

50 


4S 45 44,43 42 




0.5299 


0.6248 




0-5324 


0.6289 


1.5900 


0.8465 


2 


4-b 
0. 1 


4- 

0. 


b 4- 
8, 


♦ 4- 

B R 


3 4-2 

5 8.4 




20 


0.5348 




0.6330 




1.5798 




0.8449 




40 


3 1 


3-6 


13- 


5 13- 


2 12. 


3 12.6 




30 


0-5373 


-4 


0.6376 


40 


1.5697 


lOI 


0.8434 


16 


30 




R 7 


tR 


17. 


fii7 


2 16.8 




40 


0-5397 




0.6411 


4' 


1-5596 




0.8418 


20 


5 22.7 


22. 


5 22. 


21. 


5 21.0 




50 
33 

10 


0.5422 


24 
24 
24 


0.6453 


41 
41 
41 


1.5497 


99 
98 
97 


0.8402 


15 
16 

15 


10 
67 

50 


627.3 

731-8 
836.4 
940.9 


27- 

3^6: 

40. 


26. 

530. 
035- 

5 3Q. 


425- 

B 30. 
2 34- 
638. 


8 25.2 

I 29.4 
4 33-6 
7 37.8 




0.5448 


0.6494 


I 5398 


0.8386 




0.5471 


0.6535 


1. 5301 


0.8371 




20 


0.5495 




0.6577 




1.5204 




0.8355 




40 






30 
40 


0.5519 
0-5543 


24 


0.6619 
0.6661 


42 

42 


1.5108 
1-5013 


96 
95 


0.8339 
0.8323 


16 


30 
20 




4^ 


41 


40 


39 




50 
34 

10 


0.5568 


24 

24 
24 


0.6703 


42 
42 
42 


1-4919 


94 
93 
92 


0.8306 


»6 
16 

16 


10 
56 

50 




2 8.3 
3 12-4 

4 16.6 


8.2 

2.3 ] 

6.41 


8.0 
2.0 

6.0 


7.8 
1-7 

5.6 




0.5592 


0.674s 


1.482S 


0.8296 




0.5616 


0.6787 


1-4733 


0.8274 




20 
30 


0. 5640 
0. 5664 


24 


0.6830 
0.6873 


42 
43 


1.4641 
1.4550 


92 
91 


0.825? 
0.824T 


16 


40 
30 




5 20.7 

5 24.9 : 


0.5 20.0 19.5 
4.6 24.023.4 




40 


0.5688 


^^4 


0.6915 


42 


1.4460 


90 


0.8225 


'6 


20 




729.02 


8.7 = 


8.0: 


7-3 




50 
35 

10 


0.5712 


24 
24 
23 
24 


0.6959 


43 
43 
43 
43 
44 
44 


1.4370 


89 
89 
88 
87 
86 
86 


0.8208 


17 

16 

'6 
T7 


10 
55 

50 




3 33-2 . 
3 37-3. 


2.8 32.0131.2 

J6.936.0I35.I 




0.5736 


0.7002 


1.4281 


0.8191 


2S 25 24 23 




0.5759 


0.7045 


I. 4193 


0.8175 




20 

30 
40 


0.5783 
0.5807 
0.5830 


23 
23 


0.7089 
0.7133 
0.7177 


1. 4106 
1. 401 9 
1-3933 


0.8158 
0.8141 
0.8124 


17 
17 


40 
30 
20 




1 2.5 

2 5.1 

3 7-6 


2.5 

S.o 

7.5 


2-4 

4-8 
7.2 


2-3 

4.6 
6.9 




50 
36 

10 


0.5854 


23 
23 

2S 


0.7221 


44 
44 
44 


1-3848 


85 
84 
84 
83 
83 
81 
81 
83 
80 


0.8107 


17 
17 
17 


10 
54 

50 




4 10. 2 

5 12-7 
5 15.3 

7 17-8 1 


0.0 

2-5 1 

5.0 I 
7-S I 


9.6 
2.0 
4.4 

6.8 


9.2 

3.8 

6.x 




0.5878 


0.7265 


1-3764 


0.8090 




0. 590I 


0.7310 


1.3680 


0.8073 




20 


0.5925 




0.7354 




1-3597 


0.8056 


17 
17 
17 
17 
17 


40 




3 20.4 ! 


0.0 I 


9.2 ] 


8.4 




30 
40 

50 

37 

10 


0.5948 
0.5971 
0.5995 


23 
23 
23 
23 
23 


0.7399 

0.7444 

0.7490 


45 
4§ 
45 
45 
16 


1-3514 
1-3432 
I-3351 


0.8038 
0.8021 
0. 8004 


30 
20 
10 
53 

50 




3 22.9 : 

22 

[ 2.2 

3 6.7 


2.5 ^ 

22 

2.2 

4.4 
6.6 


18 

3-7 

5-5 


S0.7 

18 

i.S 
3.6 
5.4 




0.6018 


O.753S 


1.3276 


0.7988 




0.6041 


0.7581 


I. 3190 


0.7969 




20 


0.6064 


23 


0.7627 


46 
46 


1.3111 


78 


0.7951 




40 




t- 9.° 


R R 


7.4 


7.2 




30 


0.6087 


23 


0.7673 


1.3032 


0.7933 




30 




5 11.5 1 


3.0 


9.2 


9.0 




40 


0.61 16 


0.7719 


1.2954 




0.7916 


18 
18 
18 


20 




3 13. S 1 


3.2 1 


I.I ] 


0.8 




50 
38 

10 


0.6133 


23 
23 
23 


0.7766 


4b 
47 
47 
47 
47 


1.2876 


77 
77 

76 
76 


0.7898 


10 
52 

50 


i 


7 157 1 
5 18.0 1 


5-4 I 
7.61 

n 8 T 


2.9 1 

4.81 

fi 2 7 


2.6 

4.4 




0.6158 


0.7813 


1.2799 


0.7880 




0.6179 


0.7860 


1.2723 


0.7862 






20 
30 


0.6202 
0.6225 


22 


0.7907 
0.7954 


1.2647 
1.2571 


75 


0.7844 
0.7826 


18 


40 
30 




if 17 16 


15 

"^ T 


14 

5 1-4 

D 2.9 




40 


0.6248 




0.8002 


47 


1.2497 


74 


0.7808 




20 


2 


3.5 


3- 


4 3- 


2 3- 




50 
39 

10 
20 


0.6270 


22 

23 
22 


O.S050 


43 
48 
48 
48 


1 . 2422 


74 
73 
73 
73 


0.7789 


18 

'8 
18 


10 
51 

50 
40 


3 

4 

5 
61 


5-2 

7.0 

8-7 


5- 

6. 
8. 
10. 


1 4. 

8 6. 

5! 8. 

2 9. 


i 4- 
4 6. 
11 


5 4.3 

D 6.8 
5 7.2 
b 8.7 




0.6293 


0.8098 


I 2349 


0.7771 




0.6316 
0.6338 


0.8146 
0.8194 


1.2276 
1.2203 


0.7753 
0-7734 




30 


0.6361 




0.8243 




1.2131 




0.7716 


30 


71 


2.2 


II. 


911. 


2 10. 


5 10. 1 




40 


0.6383 




0.8292 


49 


1.2059 


71 


0.769? 


'8 


20 


91 


4.0 

S.7 


'3- 
IS- 


3 14- 


3 12. 
* 13. 


b II. 6 
5 13.0 




50 
40 


0.6405 


22 


0.8341 


1 *^ 


1. 1988 


70 


0.7679 


'§ 


10 
50 






0.6428 


0.8391 


1.1917 


0.7666 






Cos. 


d. 


Cot. 


d. 


Tan. 


d. 


Sin. 


d. 


/ e 


P. P. 





50-60 



77 



40°-45= 



TABLE V. 



40 

lO 

20 

30 
40 

50 

410 

10 
20 
30 
40 
50 
142 
10 
20 

30 

40 

50 
43 

10 
20 

30 

40 

50 
!44 

10 
20 

30 
40 

50 
45 



Sin. 
0.6428 



0.6450 
0.6472 
o. 6494 

0.65I6 
0.6538 



0.6566 

0T658T 

0.6604 
0.6626 

0.6648 

0.6669 



0.6691 

0.6713 

0.6734 

0.6756 

0.677? 
0.6798 



0.6820 




0.696? 
0.6983 
0.7009 
o. 7030 
0.7050 



0.7071 



Cos. 



Tan. 
0.8391 



o. 8440 
o. 8496 
0.8541 
0.8591 
0.8642 

0.8693 



0.8744 

0.8795 
0.884? 
0.8899 

0.8951 



0.9004 



0.9057 

0.9IIO 

0.9163 

0.9217 
0.9271 



0.9325 



0.9379 
0.9434 

0.9489 

0-9545 
0.9601 



09657 



0.9713 
0.9770 
0.9827 
0.9884 
0.9942 



1. 0000 



Cot. 




Cot. 



,191^ 



H36 
1369 

1303 
1237 
1171 



.1106 



1 041 
0977 
0913 
0849 
0786 



0723 



0661 
0599 
0538 
0476 
0416 



0355 



0295 

023§ 

0176 
0II7 
0058 



Cos. 
0.7666 



0.7641 
0.7623 
0.7604 
0.7585 
0.7566 



0-7547 



0.7528 
0.7509 
0.7489 
0.7476 
0.7451 



0-743? 



0.7412 
0.7392 
0.7373 
0.7353 
0-7333 



0-7313 



0.7293 
0.7273 
0.7253 
0.7233 
0.7213 




0.7071 



Sin. 



50 

50 
40 
30 
20 
10 

49 

50 
40 
30 
20 
10 

48 

50 
40 

30 
20 
10 

47 

50 
40 
30 
20 
10 

46 

50 

40 

30 

o 

10 

45 



p.p. 



70 


22 


22 


21 


21 


7.0 


2.2 


2.2 


2.1 


2.1 


14.0 
21.0 


6.7 


4-4 
6.6 


6.4 


4.2 

6.3, 


28.0 


9.0 


8.8 


8.6 


8.4 


35-0 


II. 2 


II. 


10.7 


IO-5 1 


42.0 


13-5 


13.2 


12.9 


12.6 1 

i 


49.0 
56.0 


15-7 
18.0 


15-4 

17.6 


iS-5 
17.2 


14-7 
16.8 


63.0 


20.2 


19.8 


19.3 


18.9 



69 


26 


20 


19 


19 


6.9 


2.0 


2.0 


1. 9 


1.9 


i3-a 
20.7 


41 
6.1 


4.0 
6.0 


3-9 

S-8 


3-8 
5-7 


27,6 


8.2 


8.0 


7.8 


7.6 


34-5 


10.2 


10. 


9-7 


9-5 


41.4 


12.3 


12.0 


11.7 


II. 4 


48.3 
55-2 
62.1 


16.4 
18.4- 


14.0 
16.0 
18.0 


'3-6 
156 
17-5 


13-3' 

15-2 

i7-il 



68 68 67 66 18 



6.8 
13-7 
20.5 

27.4 
34.2 
41. 1 

47-9 
54-8 
61.6 



6.8 


6.7 


6.6 


1-8 


13-6 
20.4 


134 
20.1 


13.2 
19.8 


3-7 

5-5 


27.2 
34-0 
40.8 


26.8 

33-5 
40.2 


26.4 
33.0 
39.6 


7-4 
9.2 
II. I 


47.6 
54-4 
61.2 


46.9 
53-6 
60.3 


46.2 
52.8 
59-4 


12.9 
14.8 
16.6 



6S 64 64 63 62 61 60 59 59 58 58 5^ 57 56 56 55 54 54 53 53 52 52 



1 

2 

3 


6.5 
•3-1 
19-6 


6.4 
12. 9 
19.3 


6.4 
12.8 
19.2 


6.3 
12.6 
18.9 


6.2 
12.4 
18.6 


6.1 
12.3 
18.4 


6.6 
12. i 
18. i 


5-9 
II. 9 

17.8 


5-9 
II. 8 
17.7 


S-S 
11.7 
17.5 


5-8 
II. 6 
17.4 


5.7 

"•5 
17.2 


5-7 
II. 4 
17. 1 


5.6 
16.9 


5.6 
II. 2 
16.8 


5.5 
II .0 
16.5 


5.4 
10.9 
16.3 


5.4 
10.8 
16.2 


5-3 
10.7 
16.0 


5-3 
10.6 
15.9 


5-2 

10.5 
15.7 


4 
5 
6 


26.2 
32.7 
39.3 


25.8 
32-2 
38.7 


25.6 
32.0 
38.4 


25.2 
31.5 
37.8 


24.8 
31.0 
37-2 


24.6 
30-7 
36.9 


24.2 
30.2 
36.3 


23.8 
29.7 
35.7 


23.6 
29.5 
35.4 


23.4 
29.2 
35.1 


23.2 
29.0 
34.8 


23.0 
28.7 
34-5 


22.8 
28.5 
34.2 


22.6 
28.2 
33.9 


22.4 
28.0 
33-6 


22.0 
27.5 
33.0 


21.8 
27.5 

32.7 


21 .6 
27.0 
32-4 


21.4 
26.7 
32.1 


21 .2 
26.5 
31.8 


21.0 
26.2 
31.5 


7 
8 

9 


45-8 
52.4 
58.9 


45-1 
51.6 
58.0 


44.8 
51.2 
57-6 


44.1 
S0.4 
56.7 


43-4 
49.6 
55-8 


43.0 
49.2 
55-3 


42.3 
48.4 
54-4 


41-6 
47.6 

53-5 


41-3 
47.2 

53-1 


40.9 
46.8 
52.6 


40.6 
46.4 
52.2 


40.2 
46.0 
51-7 


39.9 
45.6 
51.3 


39-5 
45.2 
50.8 


39.2 
44.8 
50-4 


38.5 
44.0 

49-5 


38.1 
43.6 
49 -o 


37.8 
43.2 
48.6 


37-4 
42.8 
48.1 


37.1 
42.4 
47-7 


36.7 
42.0 
47.2 



5.2 

10.4 
15-6 

20.8 
26.0 
31.2 

36.4 
41.6 
46.8 



SI SI so 50 49 



S.I 


S.I 


5.0 


5.0 


10.3 


10.2 


10. 1 


10. 


15.4 


15-3 


15-1 


15-0 


20.6 


20.4 


20.2 


20.0 


25.7 


25.5 


25.2 


25.0 


30-9 


30.6 


30.3 


30.0 


36.0 


35-7 


35.3 


35.0 


41.2 


40.8 


40.4 


40.0 


46-3 


45-9 


45-4 


45-0 



4.9 
9.9 

14-8 

19.8 
24.7 
29.7 

34.6 
39.6 
44-5 



Table for passing from Sexagesimal to Circular 
Measure. 



100 
200 
300 

40 

50 
60 

70 
80 
90 



Circular Meas. 


r 


1-74 532 9 


10 


3-49 065 8 


20 


5.23 598 8 


30 




40 


0.69 813 T 




0.87 266 4 


50 


1.04 719 j 






6 


1.22 173 


7 


1.39 626 3 


8 


1.570796 


9 



' Circular Meas. 



0.00 290 9 
0.00 581 8 
0.00 872 6 
o.oi 163 % 

o.oi 454 4 

0.00 174 % 
0.00 203 6 
0.00 232 7 
0.00 261 8 



" Circular Meas 



10 
20 
30 
40 

50 

6 

7 



45-50 



0.00 004 8 
0.00 009 7 

0.00 014 5 

0.00 019 4 

0.00 034 2 

0.00 002 9 
0.00 003 4 
0.00 003 9 
0.00 004 3 



73 



TABLE VI 



Squares and Square Roots 



OF ALL INTEGER NUMBERS 



Krom 1 TO lOOO. 



TABLE VI. 



Num. 


Square. 


Square Root. 


Num. 


Square. 


Square Root. 


I 

2 

3 


I 

4 
9 


I .0000000 
1.4142136 
1.7320508 


51 

52 
53 


26 01 
2704 
28 09 


7.1414284 
7 . 2111026 
7 . 2801099 


4 

5 
6 


16 

25 
36 


2.0000000 
2.2360680 
2.4494897 


54 

55 
56 


29 16 

3025 
31 36 


7.3484692 
7.4161985 
7.4833148 


7 
8 

: 9 


49 
64 
81 


2.6457513 
2.8284271 
3.0000000 


57 
58 
59 


3249 
3364 

3481 


7.5498344 
7.6157731 
7.6811457 


; lo 

II 

'■ 12 


I 00 
I 21 

I 44 


3.1622777 
3.3166248 
3.4641016 


60 
61 
62 


36 00 

37 21 
3844 


7.7459667 
7.8102497 
7.8740079 


i 13 

14 

i 15 


I 69 

1 96 

2 25 


3.6055513 

3.7416574 
3.8729833 


63 
64 
65 


3969 
40 96 
42 25 


7.9372539 
8.0000000 
8.0622577 


1 ^6 
17 

! i8 


2 56 

2 89 

3 24 


4.0000000 
4.1231056 
4.2426407 


66 

67 
68 


4356 
4489 
46 24 


8.1240384 
8.1853528 
8.2462113 


i ^9 

20 
' 21 


361 
4 00 
441 


4.3588989 
4.4721360 

4.5825757 


69 
70 
71 


4761 
49 00 
5041 


8.3066239 
8.3666003 
8.4261498 


1 22 

' 23 

24 


484 

5 29 
576 


4.6904158 

4.7958315 
4.8989795 


72 
73 
74 


5184 
5329 
5476 


8.4852814 
8.5440037 
8.6023253 


1 25 
! 26 

1 27 


625 
676 
7 29 


5 .0000000 
5.0990195 
5.1961524 


75 
76 

77 


5625 
57 76 
5929 


8.6602540 
8.7177979 
8.7749644 


: 28 
29 

i ^° 


784 
841 
9 00 


5.2915026 
5.3851648 
5.4772256 


78 

79 

80 


6084 
62 41 
64 00 


8.8317609 
8.8881944 
8.9442719 


, 31 
; 32 

i 33 


9 61 
10 24 

10 89 


5.5677644 
5.6568542 
5.7445626 


81 
82 
83 


6561 
67 24 
6889 


9.0000000 

9.0553851 
9.1104336 


35 

i 36 

37 
i 38 
1 39 


11 56 

12 25 
12 96 


5.8309519 
5.9160798 
6.0000000 


84 

85 
86 


7056 
72 25 
7396 


9.1651514 

9.2195445 
9.27361S5 


1369 
1444 
15 21 


6.0827625 
6. I 644 I 40 
6. 2449980 


87 
88 
89 


7569 
77 44 
7921 


9-3273791 
9-3808315 
9.4339811 


i 40 

' 41 
42 


16 00 
1681 
1764 


6.3245553 
6.4031242 
6.4807407 


90 

91 

92 


81 00 
8281 
8464 


9.4868330 
9-5393920 
9.5916630 


1 43 

! 44 
! 45 


1849 
1936 
20 25 


6.5574385 
6.6332496 
6.7082039 


93 
94 
95 


8649 
8836 
9025 


9.6436508 
9.6953597 
9-7467943 


; 46 
47 
48 


21 16 

22 09 
2304 


6.7823300 
6.8556546 
6.9282032 


96 
97 
98 


92 16 
9409 
96 04 


9.7979590 
9.8488578 
9.8994949 


49 
50 


24 01 

25 00 


7 .0000000 
7.0710678 


99 
100 


98 01 
I 00 00 


9.9498744 
10.0000000 



80 







TABLE VI. 






1 Num. 


Square. 


Square Root. 


Num. 


Square. 


Square Root. 


lOI 

102 
103 


I 02 01 
I 0404 
I 06 09 


10.0498756 
10.0995049 
10. 1488916 


151 
152 
153 


2 28 01 
2 31 04 
2 3409 


12. 2S82057 
12.3288280 
12.3693169 


104 
105 
106 


I 08 16 
I 10 25 
I 12 36 


10. 1980390 
10.2469508 
10. 2956301 


154 
155 
156 


2 37 16 

240 25 
24336 


12.4096736 j 
12.4498996 
1 2 . 4899960 


1 107 
108 
109 


I 1449 
I 16 64 

I iSSi 


10.3440804 
10.3923048 
10.4403065 


157 
158 
T59 


2 4649 
24964 

252 81 


12.5299641 
12.5698051 
12 .6095202 


1 10 
III 
112 


I 21 GO 
I 23 21 

I 25 44 


10.4880S85 

10.5356538 
10.5830052 


160 
161 
162 


2 56 00 
2 59 21 
2 62 44 


12 .6491 106 

12.6885775 
12 .7279221 


113 
114 

115 


I 27 69 
I 2996 
I 32 25 


10.6301458 
10.6770783 
10.7238053 


163 
164 
165 


265 69 
2 68 96 

2 72 25 


12.7671453 
12.8062485 
12.8452326 


116 
117 
118 


I 3456 
13689 

I 39 24 


10.7703296 
10.8166538 
10.8627805 


166 
167 
168 


2 75 56 
2 7889 
2 82 24 


12.8840987 
12.9228480 
12 .9614814 


119 
120 
121 


I 41 61 
I 44 00 
I 46 41 


10.9087121 
10.9544512 
II .0000000 


169 
170 
171 


28561 
2 89 00 
2 92 41 


13.0000000 
13.0384048 
13 .0766968 


122 
123 

124 


I 4884 
I 51 29 
I 53 76 


II. 0453610 
11.0905365 
11-1355287 


172 

173 

174 


29584 
2 99 29 
302 76 


13.1148770 

13-1529464 
13 . 1909060 


125 
126 
127 


I 5625 
15876 
I 61 29 


II. 1803399 
II .2249722 
11.2694277 


175 
176 
177 


306 25 
30976 
3 13 29 


13.2287566 
13.2664992 
13-3041347 


128 
129 
130 


16384 
I 66 41 
I 69 00 


II. 3137085 
II. 3578167 
II. 4017543 


178 
179 
180 


31684 
3 2041 
3 2400 


13-3416641 
13.3790882 
13.4164079 


131 
132 
^33 


I 71 61 

I 7424 
I 7689 


11-4455231 
II. 4891253 
11.5325626 


181 
182 
183 


3 27 61 
331 24 
33489 


13.4536240 
13-4907376 
13-5277493 


134 

135 
136 


I 7956 
I 82 25 
I 84 96 


11-5758369 
II .6189500 
II .6619038 


184 

185 
186 


33856 
342 25 
3 45 96 


13.5646600 
13.6014705 
13.6381817 


! 137 

i 138 
139 


I 87 69 
I 9044 
I 93 21 


II .7046999 
II. 7473401 
II. 7898261 


187 
188 
189 


34969 
3 53 44 
357 21 


13.6747943 
13.7113092 

13.7477271 


140 

141 

• 142 


I 96 00 

1 9881 

2 01 64 


II. 8321596 
11.8743422 
11-9163753 


190 
191 
192 


3 61 00 
36481 
36864 


13-7840488 
13.8202750 
13.8564065 


1 143 
144 

145 


2 0449 
207 36 

2 10 25 


11.9582607 
12 .0000000 
12.0415946 


193 

194 

195 


3 7249 
3 7636 
38025 


13.8924440 
13.9283883 
13.9642400 


1 146 

i 147 
148 


2 13 16 
2 16 09 
2 19 04 


12.0830460 
12.1243557 
12.1655251 


196 

197 
198 


38416 
38809 
3 92 04 


14.0000000 
14.0356688 
14.0712473 


149 
150 


2 22 01 
2 25 00 


12.2065556 
12.2474487 


199 

200 


3 9601 

4 00 00 


14. 1067360 
14.1421356 



81 







TABLE VI. 






Num. 


Square. 


Square Root. 


Num. 


Square. 


Square Root. 


20I 

202 
203 


4 04 01 
4 08 04 
4 12 09 


14.17744^9 
14.2126704 
14.2478068 


251 
252 
253 


6 30 01 

635 04 
6 40 09 


15.8429795 
15.8745079 
15-9059737 


204 
205 
206 


4 16 16 

4 20 25 
42436 


14.2828569 
14.3178211 
14.3527001 


254 

255 
256 


645 16 
65025 
65536 


15-9373775 
15.9687194 

16.0000000 


207 
208 
209 


4 2849 
432 64 
43681 


14.3874946 
14.4222051 
14.4568323 


257 
258 
259 


6 60 49 
665 64 
6 7081 


16.0312195 
16.0623784 
16.0934769 


210 
211 
212 


4 41 00 
4 45 21 
4 49 44 


14.4913767 

14.5258390 
14.5602198 


260 
261 
262 


6 76 00 
681 21 
6 8644 


16.1245155 

16.1554944 
16. 1864141 


i 213 
214 

215 


45369 
45796 
462 25 


14-5945195 
14.6287388 
14.6628783 


263 
264 
265 


6 91 69 

6 96 96 

7 02 25 


16.2172747 
16.2480768 
16.2788206 


216 
217 

! 218 


466 56 

47089 

4 75 24 


14.6969385 
14.7309199 
14.7648231 


266 
267 
268 


70756 
7 1289 
7 1824 


16.3095064 
16.3401346 
16.3707055 


219 
220 
221 


4 7961 
4 84 00 
48841 


14.7986486 
14.8323970 
14.8660687 


269 
270 
271 


7 2361 
7 29 00 
7 3441 


16.4012195 
16.4316767 
16.4620776 


222 
223 
224 


49284 

4 97 29 
501 76 


14.8996644 
14.9331845 
14.9666295 


272 
273 
274 


73984 
7 45 29 
7 5076 


16.4924225 
16.5227116 
16.5529454 


225 
226 
227 


5 06 25 
5 1076 
5 15 29 


15 .0000000 
15.0332964 
15.0665192 


275 
276 

277 


75625 
761 76 
767 29 


16.5831240 
16.6132477 
16.6433170 


228 
229 
230 


5 1984 
5 2441 
5 2900 


15 .0996689 
15.1327460 
15-1657509 


278 

279 

280 


7 7284 
77841 
7 84 00 


16.6733320 
16.7032931 
16.7332005 


231 
232 
233 


53361 
53824 
5 42 89 


15 . 1986842 
15.2315462 
15-2643375 


281 
282 
283 


7 89 61 

7 95 24 
80089 


16.7630546 
16.7928556 
16.8226038 


234 

235 
236 


54756 
552 25 
55696 


15.2970585 
15.3297097 
15.3622915 


284 
285 
286 


806 56 
8 12 25 
8 17 96 


16.8522995 
16.8819430 
16.9115345 


237 
238 
239 


5 61 69 
5 6644 
5 71 21 


15.3948043 
15.4272486 
15-4596248 


287 
288 
289 


8 23 69 
82944 
83521 


16.9410743 
16.9705627 
17 .ocooooo 


i 240 
241 
242 


5 76 00 
5 8081 
58564 


15-4919334 
15.5241747 

15-5563492 


290 
291 
292 


8 41 00 
84681 
85264 


17.0293864 
17.0587221 

17 .0880075 


243 
244 
245 


5 9049 
59536 

6 00 25 


15-5884573 
15.6204994 

15-6524758 


293 
294 
295 


85849 
86436 
87025 


17. II72428 
17. 1464282 

17-1755640 


246 
247 
248 


6 05 16 
6 10 09 
6 15 04 


15.6843871 
15-7162336 

15.7480157 


296 
297 
298 


876 16 
88209 
88804 


17 .2046505 

17.2336879 

17.2626765 


249 
250 


6 20 01 
6 25 00 


15-7797338 
15.8113883 


299 

300 


8 94 01 

9 00 00 


17. 2916165 

17.3205081 



TABLE VI. 



Num. 


Square. 


Square Boot. 


Num. 


Square. 


Square Root. 


301 

302 

303 


9 06 01 
9 12 04 
9 18 09 


17-3493516 
17.3781472 
17 .4068952 


351 
352 
353 


12 32 01 
123904 
12 46 09 


18.7349940 
18.7616630 
18.7882942 


304 

305 
306 


9 24 16 
93025 
93636 


17-4355958 
17.4642492 
17.4928557 


354 
355 
356 


1253 16 
12 60 25 
1267 36 


18.8148877 
18.8414437 
18.8679623 


307 
308 

309 


94249 
94864 

95481 


17-5214155 
17.5499288 

17-5783958 


357 
358 
359 


12 74 49 
12 81 64 
12 8881 


18.8944436 
18.9208879 
18.9472953 


310 

311 
312 


9 61 00 
9 67 21 
9 73 44 


17.6068169 
17.6351921 
17.6635217 


360 
361 
362 


12 96 00 

13 03 21 
13 1044 


18.9736660 
19.0000000 
19.0262976 


313 

314 

: 315 


97969 
98596 
992 25 


17 .6918060 
17.7200451 
17-7482393 


363 
364 
365 


13 1769 
13 2496 
1332 25 


19.0525589 
19.0787840 
19.1049732 


i 316 
317 
318 


99856 
10 04 89 
10 II 24 


17.7763888 
17.8044938 
17-8325545 


366 

367 
368 


133956 
13 46 89 

135424 


19. 131 1265 
19.1572441 
19.1833261 


1 319 

: 320 
321 


10 17 61 
10 24 00 
10 30 41 


17.8605711 
17.8885438 
17.9164729 


369 
370 
371 


13 61 61 
13 69 00 
13 76 41 


19.2093727 

19-2353841 
19.2613603 


322 
323 
324 


10 36 84 
1043 29 
10 49 76 


17-9443584 
17,9722008 
18.0000000 


372 
373 
374 


13 83 84 
13 91 29 
139876 


19.2873015 
19.3132079 
19-3390796 


1 325 
326 

! 327 


105625 
10 62 76 
10 69 29 


18.0277564 
18.0554701 
18.0831413 


375 
376 
377 


14 06 25 
14 13 76 
14 21 29 


19.3649167 
19.3907194 
19.4164878 


i 328 

1 329 

330 


10 75 84 
10 82 41 
10 89 00 


18.1107703 

18.1383571 
18. 1659021 


378 

379 
380 


14 28 84 
14 36 41 
14 44 00 


19.4422221 
19.4679223 
19-4935887 


j 331 
332 
333 


10 95 61 

11 02 24 
II 0889 


18.1934054 
18.2208672 
18.2482876 


381 

382 

383 


1451 61 
145924 
1466 89 


19.5192213 
19.5448203 
19.5703858 


334 
335 
336 


II 1556 
II 22 25 
II 28 96 


18.2756669 
18.3030052 
18.3303028 


384 

385 
386 


147456 
1482 25 
14 89 96 


19-5959179 
19.6214169 
19.6468827 


1 337 

i 33^ 

339 


II 3569 
II 4244 
II 49 21 


18.3575598 

18.3847763 
18.4119526 


387 
388 

389 


149769 
15 05 44 
15 13 21 


19.6723156 
19.6977156 
19.7230829 


340 

341 

: 342 


II 56 00 
II 62 81 
II 69 64 


18.4390889 
18.4661853 
18.4932420 


390 
391 
392 


15 21 00 
15 2881 
15 3664 


19.7484177 

19-7737199 
19.7989899 


i 343 

1 344 

345 


II 7649 
1 1 83 36 
II 90 25 


18.5202592 
18.5472370 
18.5741756 


393 

394 
395 


15 44 49 
155236 
15 6025 


19.8242276 

19-8494332 
19.8746069 


346 
347 
348 


11 97 16 

12 04 09 
12 II 04 


18.6010752 
18.6279360 
18.6547581 


396 
397 
398 


1568 16 
15 7609 
15 8404 


19.8997487 
19.9248588 
19-9499373 


349 

350 


12 18 01 
12 25 00 


18.6815417 
18.7082869 


399 
400 


15 92 01 

16 00 00 


19.9749844 
20.0000000 



83 



TABLE VI. 



Num. 


Square. 


Square Root. 


Num. 


Squai-e. 


Square Root. 


401 

402 
403 


16 08 01 
16 16 04 
16 24 09 


20.0249844 
20.0499377 
20.0748599 


451 
452 
453 


20 34 01 

20 43 04 
20 52 09 


21 .2367606 
21 .2602916 
21.2837967 


404 

405 
406 


16 32 16 
16 40 25 
164836 


20.0997512 
20. 1246118 
20.1494417 


454 
455 
456 


20 61 16 
20 70 25 
20 7936 


21.3072758 , 

21.3307290 

21.3541565 


407 
408 
409 


165649 
16 64 64 
16 72 81 


20. 1742410 
20. 1990099 
20.2237484 


457 
458 
459 


20 88 49 

20 97 64 

21 06 81 


21.3775583 
21 ,4009346 

21.4242853 1 


410 
411 
412 


16 81 00 
16 89 21 
169744 


20.2484567 
20.2731349 
20.2977831 


460 
461 
462 


21 16 00 
21 25 21 
21 3444 


21.4476106 1 
21 .4709106 
21.4941853 


413 

414 

415 


1705 69 
17 1396 

17 22 25 


20.3224014 
20.3469899 
20.3715488 


463 
464 

465 


21 4369 
21 52 96 
21 62 25 


21.5174348 [ 
21.5406592 
21.5638587 1 


416 
417 
418 


173056 
173889 
1747 24 


20.3960781 
20.4205779 
20.4450483 


466 
467 
468 


21 71 56 
21 8089 
21 90 24 


21.5870331 1 
21 .6101828 
21.6333077 


419 
420 
421 


17 55 61 
17 64 00 
17 7241 


20.4694895 
20.4939015 
20.5182845 


469 
470 
471 


21 99 61 

22 09 00 
22 18 41 


21 .6564078 
21.6794834 

21.7025344 


422 

423 

424 


178084 
17 89 29 
1797 76 


20.5426386 
20.5669638 
20.5912603 


472 
473 

474 


22 27 84 ■ 
22 37 29 
22 46 76 


21.7255610 
21.7485632 
21.7715411 


425 
426 

427 


18 g6 25 
18 14 76 
18 23 29 


20.6155281 
20.6397674 
20.6639783 


475 
476 

477 


22 56 25 
22 65 76 
22 75 29 


21.7944947 
21 .8174242 
21.8403297 1 


428 
429 
430 


18 31 84 
18 40 41 
18 49 00 


20.6881609 
20.7123152 
20.7364414 


478 

479 
480 


22 84 84 
229441 

23 04 00 


21 .863211 1 
21.8860686 
21.9089023 


431 
432 
433 


1857 61 
1866 24 
18 7489 


20.7605395 
20.7846097 
20.8086520 


481 
482 
483 


23 13 61 
23 23 24 
23 32 89 


21.9317122 
21.9544984 
21.9772610 


434 
435 
436 


188356 
1892 25 
19 00 96 


20.8326667 
20.8566536 
20.8806130 


484 
485 
486 


2342 56 
2352 25 
23 61 96 


22 .0000000 
22.0227155 
22.0454077 


437 
438 
439 


19 09 69 ' 
19 18 44 
19 27 21 


20.9045450 
20.9284495 
20.9523268 


487 
488 

489 


23 71 69 
2381 44 
23 91 21 


22.0680765 1 
22 .0907220 
22.1133444 


440 
441 
442 


19 36 00 
19 44 81 
195364 


20.9761770 
21 .0000000 
21 .0237960 


490 
491 
492 


24 01 00 
24 10 81 
24 20 64 


22.1359436 
22.1585198 
22. 1810730 


443 
444 
445 


19 62 49 
19 71 36 

198025 


21 .0475652 
21.0713075 
21.0950231 


493 
494 
495 


243049 
244036 
2450 25 


22.2036033 1 

22.2261108 

22.2485955 


446 

447 
448 


19 89 16 

19 98 09 

20 07 04 


21 . 1187121 
21.1423745 
21 . 1660105 


496 

497 
498 


24 60 16 
24 70 09 
24 80 04 


22.2710575 
22.2934968 
22.3159136 


449 
45° 


20 16 01 
20 25 00 


21 . 1896201 
21.2132034 


499 
500 


24 90 01 

25 00 00 


22.3383079 
22.3606798 , 



84 



TABLE VI. 



Num. 


Square. 


Square Root. 


Num. 


Square. 


Square Hoot. 


501 
502 
503 


25 10 01 
25 20 04 
25 30 09 


22.3830293 
22.4053565 
22.4276615 


551 
552 
553 


303601 
304704 
305809 


23-4733892 
23.4946802 
23.5159520 


504 

- 505 
506 


25 40 16 
255025 
25 6036 


22.4499443 
22.4722051 
22.4944438 


554 
555 
556 


30 69 16 
30 80 25 
3091 36 


23-5372046 
23-5584380 
23-5796522 


507 
50S 

509 
510 
511 
512 

513 
514 

515 


25 7049 
25 80 64 
25 9081 


22.5 166605 

22.5388553 
22.5610283 


557 
558 
559 


31 02 49 

31 1364 
31 2481 


23.6008474 i 

23.6220236 

23.6431808 


26 01 00 
26 II 21 
26 21 44 


22.5831796 
22 .6053091 
22 .6274170 


560 

561 
562 


31 T,6 00 
31 47 21 
3^ 5844 


23.6643191 
23-6854386 
23-7065392 


26 31 69 
26 41 96 

26 52 25 


22.6495033 
22 .6715681 
22.6936114 


563 
564 

565 


31 6969 
31 80 96 
31 92 25 


23. 7276210 
23.7486842 
23.7697286 


5^6 

517 
518 


26 62 56 
26 72 89 
26 83 24 


22.7156334 
22.7376340 
22.7596134 


566 

567 

568 


320356 
32 1489 
32 26 24 


23-7907545 
23.8117618 

23-8327506 


519 

520 

521 


26 93 61 

27 04 00 
27 14 41 


22.7815715 
22.8035085 
22.8254244 


569 
570 
571 


323761 
32 4900 
32 60 41 


23-8537209 
23.8746728 
23.8956063 


522 
523 
524 

525 
526 

527 


27 2484 
2735 29 
2745 76 


22.8473193 
22.8691933 
22.8910463 


572 
573 
574 


32 71 84 
32 83 29 
32 9476 


23.9165215 
23-9374184 i 
23.9582971 


2756 25 
27 66 76 
27 77 29 


22.9128785 
22.9346899 
22.9564806 


575 
576 
577 


S3, 06 25 
2>Z 17 76 
33 2929 


23-9791576 

24.0000000 
24.020S243 


528 
529 
530 


27 87 84 

27 9841 

28 09 00 


22.9782506 
23.0000000 
23.0217289 


578 

579 
580 


33 40 84 
335241 
33 64 00 


24.0416306 
24.0624188 
24.0831891 


531 
532 
533 
534 
535 
536 


28 1961 
2830 24 
28 40 89 


23-0434372 
23.0651252 
23.0867928 


581 
582 
583 


2>2> 75 61 
3387 24 
zs 98 89 


24.1039416 
24. 1246762 
24-1453929 


285156 
28 62 25 
28 72 96 


23. 1084400 
23. 1300670 
23-1516738 


584 
585 
586 


34 1056 
3422 25 
34 33 96 


24. 1660919 
24.1867732 
24.2074369 


537 
538 
539 


288369 
289444 
29 05 21 


23.1732605 
23.1948270 
23-2163735 


587 
588 

589 


34 45 69 
34 57 44 
3469 21 


24.2280829 
24.2487113 
24. 2693222 


540 
541 
542 

543 

544 
545 


29 16 00 
29 26 81 
2937 64 


23.2379001 
23.2594067 
23.2808935 


590 
591 
592 


34 81 00 
349281 

35 04 64 


24.2899156 
24.3104916 
24-3310501 


29 48 49 

295936 
29 70 25 


23.3023604 
23-3238076 
23-3452351 


593 
594 
595 
596 
597 
598 


35 1649 
35 2836 
35 40 25 


24-3515913 

24.3721152 
24.3926218 


546 

547 
548 


29 81 16 

29 92 09 

30 03 04 


23.3666429 
23.3880311 
23-4093998 


35 52 16 
35 64 09 
35 7604 


24.4131112 

24-4335834 
24-4540385 


549 
550 


30 1401 
30 25 00 


23-4307490 
23.4520788 


599 
600 


358801 
36 00 00 


24-4744765 
24-4948974 



85 



TABLE VI. 



1 
1 

Num. 


Square. 


Square Root. 


Num. 


Square. 


Square Root. 


6oi 
602 
' 603 
604 
605 
606 

t 607 

; 608 

609 


36 12 or 
36 24 04 
36 36 09 


24.5153013 
24.5356883 
24.5560583 


651 
652 
653 


42 3801 
42 51 04 
42 64 09 


25.5147016 
25.5342907 
25-5538647 


3648 16 
36 60 25 
36 72 36 


24.5764115 
24.5967478 
24.6170673 


654 
655 
656 


42 77 16 

42 9025 

43 03 36 


25-5734237 
25.5929678 
25 .6124969 


368449 
36 96 64 

370881 


24-6373700 
24.6576560 
24.6779254 


657 
658 

659 


43 1649 
43 29 64 
43 42 81 


25 .6320112 
25-6515107 
25-6709953 


610 
611 
612 


37 21 00 
37 33 21 

37 45 44 


24.6981781 
24.7184142 
24-7386338 


660 
661 
662 
663 
664 
665 


43 56 00 
43 69 21 
43 8244 


25.6904652 
25.7099203 
25.7293607 


613 
614 
615 


375769 
376996 

37 82 25 


24.7588368 
24.7790234 
24.7991935 


43 95 69 

44 08 96 
4422 25 


25-7487864 
25-7681975 
25-7875939 


616 

1 617 

618 


37 9456 

38 06 89 
38 19 24 


24.8193473 
24.8394847 
24.8596058 


666 
667 
668 


44 35 56 
44 48 89 
4462 24 


25-8069758 
25.8263431 
25 .8456960 


619 
620 
621 


3831 61 
384400 
385641 


24.8797 106 
24.8997992 
24.9198716 


669 
670 
671 


44 75 61 

44 89 00 

45 02 41 


25-8650343 
25.8843582 
25.9036677 


622 

623 
624 


38 68 84 
388129 
3893 76 


24-9399278 

24-9599679 
24.9799920 


672 

673 

674 


45 15 84 
45 29 29 
45 42 76 


25 .9229628 
25.9422435 
25.9615100 1 


625 
626 
627 


3906 25 
39 18 76 
3931 29 


25 .0000000 
25.0199920 
25-0399681 


675 
676 

677 


45 5625 
45 69 76 
45 83 29 


25 .9807621 
26.0000000 
26.0192237 


628 
629 
630 


39 43 84 
395641 
39 69 00 


25 .0599282 
25.0798724 
25 .0998008 


678 
679 
680 
681 
682 
683 


45 96 84 

46 10 41 
46 24 00 


26.0384331 
26.0576284 
26.0768096 


631 
i 632 

633 


3981 61 

39 94 24 

40 06 89 


25-1197134 
25.1396102 

25-1594913 


4637 61 
46 51 24 
46 64 89 


26.0959767 
26.1151297 
26.1342687 


634 

635 
636 


40 1956 
4032 25 
40 44 96 


25-1793566 
25.1992063 
25.2190404 


684 
685 
686 


467856 

46 92 25 

47 05 96 


26.1533937 
26.1725047 
26. 1916017 


637 
638 

639 


4057 69 
40 70 44 
4083 21 


25.2388589 
25.2586619 
25.2784493 


687 
688 
689 


47 1969 
47 33 44 
47 47 21 


26.2106848 
26.2297541 
26.2488095 


640 
641 

642 


40 96 00 

41 0881 
41 21 64 


25.29S2213 
25-3179778 
25-3377189 


690 
691 
692 


47 61 00 
47 7481 
47 88 64 


26. 267851 1 
26.2S68789 
26 .3058929 


! 643 
644 

645 


41 34 49 
41 47 36 

41 60 25 


25-3574447 

25-3771551 
25-3968502 


693 
694 
695 


48 02 49 
48 1636 
48 30 25 


26.3248932 
26.3438797 
26.3628527 


646 
647 
648 


41 73 16 
41 86 09 
41 9904 


25-4165301 
25.4361947 
25-4558441 


696 

697 
698 


48 44 16 

48 58 09 
48 72 04 


26.3818119 
26.4007576 
26.4196896 


1 649 
i 650 


42 12 01 
42 25 00 


25-4754784 
25-4950976 


699 

700 


488601 
49 00 00 


26.4386081 
26.4575131 



86 



TABLE VI. 



Num. 


Square. 


Square Root. 


Num. 


Square. 


Square Root. 




701 
702 
703 


49 14 01 
49 28 04 
49 42 09 


26.4764046 
26.4952826 
26.5141472 


751 

752 
753 


56 40 01 

565504 
56 7009 


27-4043792 
27 .4226184 
27.4408455 




1 704 

705 
706 

707 
708 
709 


4956 16 
49 70 25 
49 84 36 


26.5329983 
26.5518361 
26.5706605 


754 
755 
756 


56 85 16 
570025 

57 1536 


27 .4590604 
27-4772633 
27-4954542 




49 98 49 

50 12 64 
50 26 81 


26.5894716 
26.6082694 
26.6270539 


757 
758 
759 


57 3049 
57 45 64 
57 6081 


27-5136330 
27-5317998 
27-5499546 




710 
711 

1 712 


50 41 00 

5055 21 
506944 


26.6458252 
26.6645833 
26.6833281 


760 
761 
762 


57 76 00 

57 91 21 

58 06 44 


27.5680975 
27 .5862284 
27.6043475 




713 
714 
715 


50 S^ 69 
5097 96 

51 12 25 


26. 7020598 
26.7207784 
26.7394839 


763 
764 
765 


58 21 69 
583696 
5852 25 


27 .6224546 
27.6405499 
27-6586334 




716 

717 
718 


51 2656 
51 4089 
51 55 24 


26.7581763 

26.7768557 
26.7955220 


766 

767 
768 


586756 
5882 89 

589824 


27.6767050 
27 ,6947648 
27 . 7128129 




719 
720 
721 


51 6961 
51 84 00 
51 9841 


26.8141754 
26.8328157 
26.8514432 


769 
770 
771 


59 13 61 
59 2900 
594441 


27.7308492 
27-7488739 
27.7668868 




i 722 

723 
724 


52 12 84 
52 27 29 
5241 76 


26.8700577 
26.8886593 
26.9072481 


772 
773 
774 


595984 
59 75 29 
599076 


27 . 7848880 
27.8028775 
27.8208555 




725 
726 

727 


525625 
52 7076 
5285 29 


26.9258240 
26.9443872 
26.9629375 


775 
776 

777 


60 06 25 
60 21 76 
6037 29 


27.8388218 
27 -8567766 
27.8747197 




728 
729 
730 


52 9984 

53 1441 
53 2900 


26.9814751 
27.0000000 
27 .0185122 


778 

779 

780 


60 52 84 
60 68 41 
60 84 00 


27 .8926514 

27-9105715 
27 .9284801 




731 
732 
733 


534361 
535824 
53 72 89 


27.0370117 
27.0554985 
27.0739727 


781 
782 
783 


60 99 61 

61 15 24 
61 30 89 


27-9463772 
27 .9642629 
27.9821372 




734 
735 
736 


538756 
5402 25 
54 1696 


27.0924344 
27, 1108834 
27.1293199 


784 
785 
786 


61 46 56 
61 62 25 
61 77 96 


28.0000000 
28.0178515 
28.0356915 




737 
738 
739 
740 

741 
742 


5431 69 
544644 
5461 21 


27-1477439 
27. 1661554 
27.1845544 


787 
788 

789 


61 93 69 

62 09 44 
62 25 21 


28.0535203 
28.0713377 
28.0891438 




547600 

54 90 81 

55 05 64 


27. 2029410 
27.2213152 
27.2396769 


790 
791 
792 


62 41 00 
62 56 81 
62 72 64 


28. 1069386 
28. 1247222 
28. 1424946 




743 
744 
745 


55 2049 
55 35 36 
555025 


27.2580263 
27.2763634 
27.2946881 


793 
794 

795 


62 8849 

63 04 36 
63 20 25 


28. 1602557 
28. 1780056 
28.1957444 




746 

747 
748 


5565 16 
55 8009 
55 95 04 


27.3130006 
27-3313007 
27.3495887 


796 

797 
798 


63 36 16 
6352 09 
63 68 04 


28.2134720 
28.2311884 
28.2488938 




749 

750 


56 10 01 
56 25 00 


27.3678644 
27.3861279 


799 
800 


63 84 01 

64 00 00 


28.2665881 
28.2842712 





87 



TABLE VI. 



Num. 


Square. 


Square Root. 


Num. 


Square. 


Square Root. 


Soi 
802 
803 


64 16 01 
64 32 04 
64 48 09 


28.3019434 
28.3196045 
28.3372546 


851 
852 

853 


72 42 01 
725904 
72 76 09 


29.1719043 
29. 1890390 
29. 2061637 


804 
805 
806 


64 64 16 
64 80 25 
6496 s6 


28.3548938 
28.3725219 
28.3901391 


854 

855 
856 


72 93 16 

73 1025 
73 27 36 


29. 2232784 
29.2403830 
29-2574777 


807 
808 
809 


65 1249 
65 2864 
65 44 81 


28.4077454 
28.4253408 
28.4429253 


857 
858 

859 


73 44 49 
7361 64 
737881 


29.2745623 
29.2916370 
29.3087018 


810 
811 
812 


65 61 00 
65 77 21 
65 93 44 


28.4604989 
28.4780617 
28.4956137 


860 
861 
862 


73 9600 

74 13 21 

74 30 44 


29-3257566 
29.3428015 
29-3598365 1 


813 
814 

815 


66 09 69 
66 25 96 
66 42 25 


28.5131549 
28.5306852 
28.5482048 


863 
864 
865 


74 47 69 
74 64 96 
7482 25 


29.3768616 

29-3938769 
29.4108823 


816 
817 
818 


665856 
66 74 89 
66 91 24 


28.5657137 
28.5832119 
28.6006993 


866 
867 
868 


749956 
75 1689 
75 3424 


29.4278779 
29.4448637 
29.4618397 


819 
820 
821 


67 07 61 
67 24 00 
67 40 41 


28.6181760 
28.6356421 
28.6530976 


869 
870 
871 


75 51 61 
75 69 00 
758641 


29.4788059 
29.4957624 
29.5127091 


822 
823 
824 


675684 
67 73 29 
67 8976 


28.6705424 
28.6879766 
28.7054002 


872 

873 
874 


76 03 84 
76 21 29 
763876 


29.5296461 

29-5465734 
29.5634910 


825 
826 

827 


68 06 25 
6822 76 
6839 29 


28.7228132 
28.7402157 
28.7576077 


875 
876 

877 


765625 

7673 76 
76 91 29 


29-5803989 
29.5972972 
29.6141858 


828 
829 
830 


685584 
68 72 41 
68 89 00 


28.7749891 
28.7923601 
28.8097206 


878 
879 
880 


77 08 84 
77 2641 
774400 


29.6310648 
29.6479342 
29.6647939 


831 
832 

833 


69 05 61 
69 22 24 
69 38 89 


28.8270706 
28.8444102 
28.8617394 


881 
882 
883 


77 61 61 

77 7924 
779689 


29.6816442 
29.6984848 
29-7153159 


834 

835 
836 


695556 
69 72 25 
698896 


28.8790582 
28.8963666 
28.9136646 


884 
885 
886 


78 1456 
783225 
78 49 96 


29-7321375 
29.7489496 

29-7657521 


837 
838 

839 


7005 69 
702244 
703921 


28.9309523 
28.9482297 
28.9654967 


887 
888 
889 


786769 
78 85 44 
7903 21 


29.7825452 
29.7993289 
29.8161030 


840 
841 
842 


70 56 00 
70 72 81 
70 89 64 


28.9827535 
29.0000000 
29.0172363 


890 
891 
892 


79 21 00 
793881 
795664 


29.8328678 
29.8496231 
29.8663690 


843 
844 
845 


71 06 49 
71 2336 

71 4025 


29.0344623 
29.0516781 
29.0688837 


893 
894 
895 


79 74 49 
799236 

80 10 25 


29.8831056 
29.8998328 
29.9165506 


846 

847 
848 


71 57 16 
71 7409 
71 91 04 


29.0860791 
29.1032644 
29. 1204396 


896 

897 
898 


80 28 16 
80 46 09 
80 64 04 


29-9332591 
29.9499583 
29.9666481 


849 
850 


72 08 01 
72 25 00 


29. 1376046 
29-1547595 


899 
900 


808201 
81 00 00 


29.9833287 
30.0000000 



88 



TABLE VI. 



Num. 


Square. 


Square Root. 


Num. 


Square. 


Square Koot. 


901 
902 
903 


Si 1801 
81 3604 
81 5409 


30.0166620 
30.0333148 
30.0499584 


951 
952 
953 


90 44 01 
90 63 04 
90 82 09 


30.8382879 
30.8544972 
30.8706981 


904 

905 
906 

907 
908 
909 
910 

I 911 
912 


81 72 16 

81 90 25 

82 oS 36 


30.0665928 
30.0832179 
30.099S339 


954 
955 
956 


91 01 16 

91 20 25 
91 3936 


30.8868904 
30.9030743 
30.9192497 


82 26 49 
82 44 64 
82 62 81 


30.1164407 

30-1330383 
30. 1496269 


957 
958 
959 


91 5849 
91 7764 
91 96 81 


30.9354166 

30.9515751 
30.9677251 


82 8i 00 
82 99 21 
S3 17 44 


30. 1662063 
30.1827765 
30.1993377 


960 
961 
962 


92 16 00 
9235 21 
925444 


30.9838668 
31 .0000000 
31 .0161248 


913 
914 

! 915 


83 35 69 
83 53 96 
8372 25 


30.2158899 
30.2324329 
30. 2489669 


963 
964 
965 


92 7369 

92 92 96 

93 12 25 


31.0322413 
31.0483494 
31.0644491 


916 
917 
918 
919 
920 
921 


83 90 56 

84 08 89 
8427 24 


30.2654919 
30.2820079 
30.2985148 


966 

967 
968 


93 3^ 56 
93 50 89 
93 7024 


31.0805405 
31.0966236 
31.1126984 


8445 61 
84 64 00 
848241 


30.3150128 
30.3315018 
30.3479818 


969 
970 
971 


93 8961 

94 09 00 
94 28 41 


31 . 1287648 
31.1448230 
31 . 1608729 


922 

923 
924 

925 
926 

; 427 


85 00 84 
85 1929 
85 37 76 


30.3644529 
30.3809151 
30.3973683 


972 

973 
974 


94 47 84 
9467 29 
94 86 76 


31.1769145 
31.1929479 
31.2089731 


85 56 25 
85 74 76 
85 93 29 


30.4138127 
30.4302481 
30.4466747 


975 
976 
977 


95 06 25 
95 25 76 
95 45 29 


31.2249900 
31.2409987 
31.2569992 


; 928 
929 
930 


86 II 84 
86 30 41 

86 49 00 


30.4630924 
30.4795013 
30.4959014 


978 

979 
980 


95 64 84 

95 8441 

96 04 00 


31.2729915 
31.2889757 
31.3049517 


! 931 

: 932 
933 


8667 61 

86 86 24 

87 04 89 


30.5122926 
30.5286750 
30.5450487 


981 
982 
983 


96 23 61 
96 43 24 
96 62 89 


31.3209195 
31.3368792 
31.3528308 


; 934 

! 935 
! 936 


872356 
8742 25 
87 60 96 


30.5614136 
30.5777697 
30.5941171 


984 

985 
986 


9682 56 
97 02 25 
97 21 96 


31.3687743 
31.3847097 
31.4006369 


937 

938 

1 939 


87 7969 

87 98 44 

88 17 21 


30.6104557 
30.6267857 
30.6431069 


987 
988 
989 


9741 69 
9761 44 
97 8r, 21 


31.4165561 
31.4324673 

31.4483704 


940 
941 
942 


88 36 00 
885481 
88 73 64 


30.6594194 
30.6757233 
30.6920185 


990 
991 

992 


98 01 00 
98 2081 
98 40 64 


31.4642654 
31.4801525 
31.4960315 


943 

944 

! 945 


88 92 49 

89 II 36 
893025 


30.7083051 
30.7245830 
30.7408523 


993 
994 
995 


98 60 49 
98 80 36 
9900 25 


31.5119025 

31.5277655 
31.5436206 


946 

947 
948 


89 49 16 
89 68 og 
89 87 04 


30.7571130 

30.7733651 
30.7896086 


996 

997 
998 


99 20 16 

99 40 09 
99 60 04 


31.5594677 
31.5753068 
31.5911380 


i 949 
1 95° 


90 06 01 
90 25 00 


30.8058436 
30.8220700 


999 
1000 


99 80 01 

I 00 00 00 


31 .6069613 
31.6227766 



OT CALKORNI^ 



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